Daily Papers

Video predictive models are emerging as a powerful paradigm in robotics, offering a promising path toward task generalization, long-horizon planning, and flexible decision-making. However, prevailing approaches often operate on 2D video sequences, inherently lacking the 3D geometric understanding necessary for precise spatial reasoning and physical consistency. We introduce a Structured 4D Latent Predictive Model, which predicts the evolution of a scene's 3D structure in a structured latent space conditioned on observations and textual instructions. Our representation encodes the scene holistically and can be decoded into diverse 3D formats, enabling a more complete and 3D consistent scene understanding. This structured 4D latent predictive model serves as a planner, generating future scenes that are translated into executable actions by a goal-conditioned inverse dynamics module. Experiments demonstrate that our model generates futures with strong visual quality, substantially better 3D consistency and multi-view coherence compared to state-of-the-art video-based planners. Consequently, our full planning pipeline achieves superior performance on complex manipulation tasks, exhibits robust generalization to novel visual conditions, and proves effective on real-world robotic platforms. Our website is available at https://structured-4d-model.github.io/.

4D generation synthesizes dynamic 3D scenes from conditions such as text or images. Existing methods either reconstruct generated RGB videos with a separate 4D model or adapt a particular video generator to predict geometry directly. The former suffers from distribution mismatch and error propagation, whereas the latter ties 4D prediction to a specific generator and may require retraining when the generator or conditioning regime changes. We ask whether the final denoised latents of video models that share a variational autoencoder (VAE) can instead provide a reusable interface to explicit 4D prediction. Building on this insight, we introduce direct latent-to-4D generation and instantiate it as Latent-to-4D, which bypasses RGB by aligning a video latent with the token grid of a pretrained 4D decoder and refining it through frame-wise and global spatiotemporal attention. Trained on roughly 1K existing reconstruction clips, a single checkpoint transfers unchanged across multiple video diffusion transformers within the same VAE family. On Text4D-200 and I4D-200, Latent-to-4D surpasses matched same-latent Wan+4RC cascades in projection-based DINO-F1 by 2.88--3.45 and 5.81 points, respectively, while also being preferred by human raters for geometry, temporal stability, and overall quality.

Directly learning to model 4D content, including shape, color and motion, is challenging. Existing methods depend on skeleton-based motion control and offer limited continuity in detail. To address this, we propose a novel framework that generates coherent 4D sequences with animation of 3D shapes under given conditions with dynamic evolution of shape and color over time through integrative latent mapping. We first employ an integrative latent unified representation to encode shape and color information of each detailed 3D geometry frame. The proposed skeleton-free latent 4D sequence joint representation allows us to leverage diffusion models in a low-dimensional space to control the generation of 4D sequences. Finally, temporally coherent 4D sequences are generated conforming well to the input images and text prompts. Extensive experiments on the ShapeNet, 3DBiCar and DeformingThings4D datasets for several tasks demonstrate that our method effectively learns to generate quality 3D shapes with color and 4D mesh animations, improving over the current state-of-the-art. Source code will be released.

We present SS4D, a native 4D generative model that synthesizes dynamic 3D objects directly from monocular video. Unlike prior approaches that construct 4D representations by optimizing over 3D or video generative models, we train a generator directly on 4D data, achieving high fidelity, temporal coherence, and structural consistency. At the core of our method is a compressed set of structured spacetime latents. Specifically, (1) To address the scarcity of 4D training data, we build on a pre-trained single-image-to-3D model, preserving strong spatial consistency. (2) Temporal consistency is enforced by introducing dedicated temporal layers that reason across frames. (3) To support efficient training and inference over long video sequences, we compress the latent sequence along the temporal axis using factorized 4D convolutions and temporal downsampling blocks. In addition, we employ a carefully designed training strategy to enhance robustness against occlusion

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.

Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and the expanded availability of experimental 3D protein structures have accelerated structure prediction, the dynamic nature of protein structures has received limited attention. This study introduces an innovative 4D diffusion model incorporating molecular dynamics (MD) simulation data to learn dynamic protein structures. Our approach is distinguished by the following components: (1) a unified diffusion model capable of generating dynamic protein structures, including both the backbone and side chains, utilizing atomic grouping and side-chain dihedral angle predictions; (2) a reference network that enhances structural consistency by integrating the latent embeddings of the initial 3D protein structures; and (3) a motion alignment module aimed at improving temporal structural coherence across multiple time steps. To our knowledge, this is the first diffusion-based model aimed at predicting protein trajectories across multiple time steps simultaneously. Validation on benchmark datasets demonstrates that our model exhibits high accuracy in predicting dynamic 3D structures of proteins containing up to 256 amino acids over 32 time steps, effectively capturing both local flexibility in stable states and significant conformational changes.

3D Gaussian Splatting (3DGS) has emerged as an efficient and high-fidelity paradigm for novel view synthesis. To adapt 3DGS for dynamic content, deformable 3DGS incorporates temporally deformable primitives with learnable latent embeddings to capture complex motions. Despite its impressive performance, the high-dimensional embeddings and vast number of primitives lead to substantial storage requirements. In this paper, we introduce a Lightweight 4DGS framework, called Light4GS, that employs significance pruning with a deep context model to provide a lightweight storage-efficient dynamic 3DGS representation. The proposed Light4GS is based on 4DGS that is a typical representation of deformable 3DGS. Specifically, our framework is built upon two core components: (1) a spatio-temporal significance pruning strategy that eliminates over 64\% of the deformable primitives, followed by an entropy-constrained spherical harmonics compression applied to the remainder; and (2) a deep context model that integrates intra- and inter-prediction with hyperprior into a coarse-to-fine context structure to enable efficient multiscale latent embedding compression. Our approach achieves over 120x compression and increases rendering FPS up to 20\% compared to the baseline 4DGS, and also superior to frame-wise state-of-the-art 3DGS compression methods, revealing the effectiveness of our Light4GS in terms of both intra- and inter-prediction methods without sacrificing rendering quality.

Developing robust artificial intelligence models for 4D (3D + time) medical imaging is constrained by limited annotated data, inter-device domain shifts, and privacy restrictions. To address this, we propose a 4D controllable generative framework for anatomically consistent data augmentation. A semi-supervised variational autoencoder learns a compact latent representation of anatomical volumes while jointly predicting aligned segmentation masks in a unified framework. Anatomical structure is then disentangled from temporal dynamics through a cascaded latent diffusion model (LDM). A static LDM generates subject-specific anatomy conditioned on clinical priors (diagnosis and volumes measures) and a subsequent motion LDM estimates residual latent motions, ensuring strict temporal coherence across the 4D sequence. The proposed approach was evaluated on cine cardiac MRI as a representative 4D imaging application. Experiments across multiple datasets demonstrate high controllability of static anatomy (Pearson r > 0.8) and strong temporal coherence (FVD = 288.08). In cross-vendor generalization experiments, augmenting training sets with synthetic 4D sequences significantly improves downstream segmentation performance. Using nnU-Net, the proposed augmentation strategy improves the average Dice score by 1.4% and reduces the Hausdorff Distance by 3.0mm compared to training on real data alone, for the left ventricle, Dice improves by 2.8% with a 5.4mm reduction in boundary error. Overall, this framework provides a scalable and controllable solution for 4D medical image synthesis, supporting the development of more robust models with limited annotations and cross-vendor variability. Code available on https://github.com/cyiheng/4DCardiacMRISynthesis.

Aided by text-to-image and text-to-video diffusion models, existing 4D content creation pipelines utilize score distillation sampling to optimize the entire dynamic 3D scene. However, as these pipelines generate 4D content from text or image inputs, they incur significant time and effort in prompt engineering through trial and error. This work introduces 4DGen, a novel, holistic framework for grounded 4D content creation that decomposes the 4D generation task into multiple stages. We identify static 3D assets and monocular video sequences as key components in constructing the 4D content. Our pipeline facilitates conditional 4D generation, enabling users to specify geometry (3D assets) and motion (monocular videos), thus offering superior control over content creation. Furthermore, we construct our 4D representation using dynamic 3D Gaussians, which permits efficient, high-resolution supervision through rendering during training, thereby facilitating high-quality 4D generation. Additionally, we employ spatial-temporal pseudo labels on anchor frames, along with seamless consistency priors implemented through 3D-aware score distillation sampling and smoothness regularizations. Compared to existing baselines, our approach yields competitive results in faithfully reconstructing input signals and realistically inferring renderings from novel viewpoints and timesteps. Most importantly, our method supports grounded generation, offering users enhanced control, a feature difficult to achieve with previous methods. Project page: https://vita-group.github.io/4DGen/

Being able to predict what may happen in the future requires an in-depth understanding of the physical and causal rules that govern the world. A model that is able to do so has a number of appealing applications, from robotic planning to representation learning. However, learning to predict raw future observations, such as frames in a video, is exceedingly challenging -- the ambiguous nature of the problem can cause a naively designed model to average together possible futures into a single, blurry prediction. Recently, this has been addressed by two distinct approaches: (a) latent variational variable models that explicitly model underlying stochasticity and (b) adversarially-trained models that aim to produce naturalistic images. However, a standard latent variable model can struggle to produce realistic results, and a standard adversarially-trained model underutilizes latent variables and fails to produce diverse predictions. We show that these distinct methods are in fact complementary. Combining the two produces predictions that look more realistic to human raters and better cover the range of possible futures. Our method outperforms prior and concurrent work in these aspects.

We present 4DNeX, the first feed-forward framework for generating 4D (i.e., dynamic 3D) scene representations from a single image. In contrast to existing methods that rely on computationally intensive optimization or require multi-frame video inputs, 4DNeX enables efficient, end-to-end image-to-4D generation by fine-tuning a pretrained video diffusion model. Specifically, 1) to alleviate the scarcity of 4D data, we construct 4DNeX-10M, a large-scale dataset with high-quality 4D annotations generated using advanced reconstruction approaches. 2) we introduce a unified 6D video representation that jointly models RGB and XYZ sequences, facilitating structured learning of both appearance and geometry. 3) we propose a set of simple yet effective adaptation strategies to repurpose pretrained video diffusion models for 4D modeling. 4DNeX produces high-quality dynamic point clouds that enable novel-view video synthesis. Extensive experiments demonstrate that 4DNeX outperforms existing 4D generation methods in efficiency and generalizability, offering a scalable solution for image-to-4D modeling and laying the foundation for generative 4D world models that simulate dynamic scene evolution.

We propose Mesh4D, a feed-forward model for monocular 4D mesh reconstruction. Given a monocular video of a dynamic object, our model reconstructs the object's complete 3D shape and motion, represented as a deformation field. Our key contribution is a compact latent space that encodes the entire animation sequence in a single pass. This latent space is learned by an autoencoder that, during training, is guided by the skeletal structure of the training objects, providing strong priors on plausible deformations. Crucially, skeletal information is not required at inference time. The encoder employs spatio-temporal attention, yielding a more stable representation of the object's overall deformation. Building on this representation, we train a latent diffusion model that, conditioned on the input video and the mesh reconstructed from the first frame, predicts the full animation in one shot. We evaluate Mesh4D on reconstruction and novel view synthesis benchmarks, outperforming prior methods in recovering accurate 3D shape and deformation.

View-predictive generative models provide strong priors for lifting object-centric images and videos into 3D and 4D through rendering and score distillation objectives. A question then remains: what about lifting complete multi-object dynamic scenes? There are two challenges in this direction: First, rendering error gradients are often insufficient to recover fast object motion, and second, view predictive generative models work much better for objects than whole scenes, so, score distillation objectives cannot currently be applied at the scene level directly. We present DreamScene4D, the first approach to generate 3D dynamic scenes of multiple objects from monocular videos via 360-degree novel view synthesis. Our key insight is a "decompose-recompose" approach that factorizes the video scene into the background and object tracks, while also factorizing object motion into 3 components: object-centric deformation, object-to-world-frame transformation, and camera motion. Such decomposition permits rendering error gradients and object view-predictive models to recover object 3D completions and deformations while bounding box tracks guide the large object movements in the scene. We show extensive results on challenging DAVIS, Kubric, and self-captured videos with quantitative comparisons and a user preference study. Besides 4D scene generation, DreamScene4D obtains accurate 2D persistent point track by projecting the inferred 3D trajectories to 2D. We will release our code and hope our work will stimulate more research on fine-grained 4D understanding from videos.

Can we scale 4D pretraining to learn general space-time representations that reconstruct an object from a few views at some times to any view at any time? We provide an affirmative answer with 4D-LRM, the first large-scale 4D reconstruction model that takes input from unconstrained views and timestamps and renders arbitrary novel view-time combinations. Unlike prior 4D approaches, e.g., optimization-based, geometry-based, or generative, that struggle with efficiency, generalization, or faithfulness, 4D-LRM learns a unified space-time representation and directly predicts per-pixel 4D Gaussian primitives from posed image tokens across time, enabling fast, high-quality rendering at, in principle, infinite frame rate. Our results demonstrate that scaling spatiotemporal pretraining enables accurate and efficient 4D reconstruction. We show that 4D-LRM generalizes to novel objects, interpolates across time, and handles diverse camera setups. It reconstructs 24-frame sequences in one forward pass with less than 1.5 seconds on a single A100 GPU.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

Current 4D generation methods have achieved noteworthy efficacy with the aid of advanced diffusion generative models. However, these methods lack multi-view spatial-temporal modeling and encounter challenges in integrating diverse prior knowledge from multiple diffusion models, resulting in inconsistent temporal appearance and flickers. In this paper, we propose a novel 4D generation pipeline, namely 4Diffusion aimed at generating spatial-temporally consistent 4D content from a monocular video. We first design a unified diffusion model tailored for multi-view video generation by incorporating a learnable motion module into a frozen 3D-aware diffusion model to capture multi-view spatial-temporal correlations. After training on a curated dataset, our diffusion model acquires reasonable temporal consistency and inherently preserves the generalizability and spatial consistency of the 3D-aware diffusion model. Subsequently, we propose 4D-aware Score Distillation Sampling loss, which is based on our multi-view video diffusion model, to optimize 4D representation parameterized by dynamic NeRF. This aims to eliminate discrepancies arising from multiple diffusion models, allowing for generating spatial-temporally consistent 4D content. Moreover, we devise an anchor loss to enhance the appearance details and facilitate the learning of dynamic NeRF. Extensive qualitative and quantitative experiments demonstrate that our method achieves superior performance compared to previous methods.

We present 4RC, a unified feed-forward framework for 4D reconstruction from monocular videos. Unlike existing approaches that typically decouple motion from geometry or produce limited 4D attributes such as sparse trajectories or two-view scene flow, 4RC learns a holistic 4D representation that jointly captures dense scene geometry and motion dynamics. At its core, 4RC introduces a novel encode-once, query-anywhere and anytime paradigm: a transformer backbone encodes the entire video into a compact spatio-temporal latent space, from which a conditional decoder can efficiently query 3D geometry and motion for any query frame at any target timestamp. To facilitate learning, we represent per-view 4D attributes in a minimally factorized form by decomposing them into base geometry and time-dependent relative motion. Extensive experiments demonstrate that 4RC outperforms prior and concurrent methods across a wide range of 4D reconstruction tasks.

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise (varepsilon) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation that accommodates arbitrary output targets, of which varepsilon-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, while our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations. More detailed information can be found at https://vveicao.github.io/projects/Motion2VecSets/.

Recent breakthroughs in 3D generative modeling have yielded remarkable progress in static shape synthesis, yet high-fidelity dynamic 4D generation remains elusive, hindered by temporal artifacts and prohibitive computational demand. We present Sculpt4D, a native 4D generative framework that seamlessly integrates efficient temporal modeling into a pretrained 3D Diffusion Transformer (Hunyuan3D 2.1), thereby mitigating the scarcity of 4D training data. At its core lies a Block Sparse Attention mechanism that preserves object identity by anchoring to the initial frame while capturing rich motion dynamics via a time-decaying sparse mask. This design faithfully models complex spatiotemporal dependencies with high fidelity, while sidestepping the quadratic overhead of full attention and reducing network total computation by 56%. Consequently, Sculpt4D establishes a new state-of-the-art in temporally coherent 4D synthesis and charts a path toward efficient and scalable 4D generation.

Forecasting from partial observations is central to world modeling. Many recent methods represent the world through images, and reduce forecasting to stochastic video generation. Although such methods excel at realism and visual fidelity, predicting pixels is computationally intensive and not directly useful in many applications, as it requires translating RGB into signals useful for decision making. An alternative approach uses features from vision foundation models (VFMs) as world representations, performing deterministic regression to predict future world states. These features can be directly translated into actionable signals such as semantic segmentation and depth, while remaining computationally efficient. However, deterministic regression averages over multiple plausible futures, undermining forecast accuracy by failing to capture uncertainty. To address this crucial limitation, we introduce a generative forecaster that performs autoregressive flow matching in VFM feature space. Our key insight is that generative modeling in this space requires encoding VFM features into a compact latent space suitable for diffusion. We show that this latent space preserves information more effectively than previously used PCA-based alternatives, both for forecasting and other applications, such as image generation. Our latent predictions can be easily decoded into multiple useful and interpretable output modalities: semantic segmentation, depth, surface normals, and even RGB. With matched architecture and compute, our method produces sharper and more accurate predictions than regression across all modalities. Our results suggest that stochastic conditional generation of VFM features offers a promising and scalable foundation for future world models.

Humans are born with vision-based 4D spatial-temporal intelligence, which enables us to perceive and reason about the evolution of 3D space over time from purely visual inputs. Despite its importance, this capability remains a significant bottleneck for current multimodal large language models (MLLMs). To tackle this challenge, we introduce MLLM-4D, a comprehensive framework designed to bridge the gaps in training data curation and model post-training for spatiotemporal understanding and reasoning. On the data front, we develop a cost-efficient data curation pipeline that repurposes existing stereo video datasets into high-quality 4D spatiotemporal instructional data. This results in the MLLM4D-2M and MLLM4D-R1-30k datasets for Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT), alongside MLLM4D-Bench for comprehensive evaluation. Regarding model training, our post-training strategy establishes a foundational 4D understanding via SFT and further catalyzes 4D reasoning capabilities by employing Group Relative Policy Optimization (GRPO) with specialized Spatiotemporal Chain of Thought (ST-CoT) prompting and Spatiotemporal reward functions (ST-reward) without involving the modification of architecture. Extensive experiments demonstrate that MLLM-4D achieves state-of-the-art spatial-temporal understanding and reasoning capabilities from purely 2D RGB inputs. Project page: https://github.com/GVCLab/MLLM-4D.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their own latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. Such a grammar generates strings of visible tokens by recursively applying production rules along a tree of hidden symbols of depth L. For such data, supervised or token-level SSL require a number of samples exponential in L to recover the latent tree; we prove that latent prediction achieves this with a number of samples constant in L, up to logarithmic factors. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

The availability of large-scale multimodal datasets and advancements in diffusion models have significantly accelerated progress in 4D content generation. Most prior approaches rely on multiple image or video diffusion models, utilizing score distillation sampling for optimization or generating pseudo novel views for direct supervision. However, these methods are hindered by slow optimization speeds and multi-view inconsistency issues. Spatial and temporal consistency in 4D geometry has been extensively explored respectively in 3D-aware diffusion models and traditional monocular video diffusion models. Building on this foundation, we propose a strategy to migrate the temporal consistency in video diffusion models to the spatial-temporal consistency required for 4D generation. Specifically, we present a novel framework, Diffusion4D, for efficient and scalable 4D content generation. Leveraging a meticulously curated dynamic 3D dataset, we develop a 4D-aware video diffusion model capable of synthesizing orbital views of dynamic 3D assets. To control the dynamic strength of these assets, we introduce a 3D-to-4D motion magnitude metric as guidance. Additionally, we propose a novel motion magnitude reconstruction loss and 3D-aware classifier-free guidance to refine the learning and generation of motion dynamics. After obtaining orbital views of the 4D asset, we perform explicit 4D construction with Gaussian splatting in a coarse-to-fine manner. The synthesized multi-view consistent 4D image set enables us to swiftly generate high-fidelity and diverse 4D assets within just several minutes. Extensive experiments demonstrate that our method surpasses prior state-of-the-art techniques in terms of generation efficiency and 4D geometry consistency across various prompt modalities.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

The synthesis of spatiotemporally coherent 4D content presents fundamental challenges in computer vision, requiring simultaneous modeling of high-fidelity spatial representations and physically plausible temporal dynamics. Current approaches often struggle to maintain view consistency while handling complex scene dynamics, particularly in large-scale environments with multiple interacting elements. This work introduces Dream4D, a novel framework that bridges this gap through a synergy of controllable video generation and neural 4D reconstruction. Our approach seamlessly combines a two-stage architecture: it first predicts optimal camera trajectories from a single image using few-shot learning, then generates geometrically consistent multi-view sequences via a specialized pose-conditioned diffusion process, which are finally converted into a persistent 4D representation. This framework is the first to leverage both rich temporal priors from video diffusion models and geometric awareness of the reconstruction models, which significantly facilitates 4D generation and shows higher quality (e.g., mPSNR, mSSIM) over existing methods.

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE). We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.

Scenes in the real world are often composed of several static and dynamic objects. Capturing their 4-dimensional structures, composition and spatio-temporal configuration in-the-wild, though extremely interesting, is equally hard. Therefore, existing works often focus on one object at a time, while relying on some category-specific parametric shape model for dynamic objects. This can lead to inconsistent scene configurations, in addition to being limited to the modeled object categories. We propose COM4D (Compositional 4D), a method that consistently and jointly predicts the structure and spatio-temporal configuration of 4D/3D objects using only static multi-object or dynamic single object supervision. We achieve this by a carefully designed training of spatial and temporal attentions on 2D video input. The training is disentangled into learning from object compositions on the one hand, and single object dynamics throughout the video on the other, thus completely avoiding reliance on 4D compositional training data. At inference time, our proposed attention mixing mechanism combines these independently learned attentions, without requiring any 4D composition examples. By alternating between spatial and temporal reasoning, COM4D reconstructs complete and persistent 4D scenes with multiple interacting objects directly from monocular videos. Furthermore, COM4D provides state-of-the-art results in existing separate problems of 4D object and composed 3D reconstruction despite being purely data-driven.

Recent advancements in diffusion models for 2D and 3D content creation have sparked a surge of interest in generating 4D content. However, the scarcity of 3D scene datasets constrains current methodologies to primarily object-centric generation. To overcome this limitation, we present Comp4D, a novel framework for Compositional 4D Generation. Unlike conventional methods that generate a singular 4D representation of the entire scene, Comp4D innovatively constructs each 4D object within the scene separately. Utilizing Large Language Models (LLMs), the framework begins by decomposing an input text prompt into distinct entities and maps out their trajectories. It then constructs the compositional 4D scene by accurately positioning these objects along their designated paths. To refine the scene, our method employs a compositional score distillation technique guided by the pre-defined trajectories, utilizing pre-trained diffusion models across text-to-image, text-to-video, and text-to-3D domains. Extensive experiments demonstrate our outstanding 4D content creation capability compared to prior arts, showcasing superior visual quality, motion fidelity, and enhanced object interactions.

Data-driven approaches have revolutionized 3D vision, enabling transformers to effectively reconstruct and generate static 3D objects. However, generating simulative 4D dynamics -- realistic temporal deformations of static objects under various physical conditions -- remains challenging and often ad hoc, despite its importance in building comprehensive 3D world models. Most existing methods assume a predefined physical model and use system identification to estimate parameters, restricting these methods to specific categories and small-scale datasets. We propose that these restrictions can be overcome by learning a data-driven kinematic state parameterization for object-centric physical systems. Specifically, we learn both a latent space representing all possible states of the object and a decoder that maps any sampled latent to a plausibly deformed shape of the object. We refer to this parameterization as Neural Object Kinematics (NeuROK), and learn a transformer-based encoder-decoder model on a curated large-scale 4D dataset. This formulation and the learned model significantly simplify the generation of simulative dynamics since we only need to consider the dynamics within a low-dimensional latent space from the Lagrangian mechanics' perspective in classical physics. We demonstrate the effectiveness and generality of this neural simulation framework across diverse dynamic object types, showing clear advantages over prior works. Project page: https://chen-geng.com/neurok

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

We present 4DiM, a cascaded diffusion model for 4D novel view synthesis (NVS), conditioned on one or more images of a general scene, and a set of camera poses and timestamps. To overcome challenges due to limited availability of 4D training data, we advocate joint training on 3D (with camera pose), 4D (pose+time) and video (time but no pose) data and propose a new architecture that enables the same. We further advocate the calibration of SfM posed data using monocular metric depth estimators for metric scale camera control. For model evaluation, we introduce new metrics to enrich and overcome shortcomings of current evaluation schemes, demonstrating state-of-the-art results in both fidelity and pose control compared to existing diffusion models for 3D NVS, while at the same time adding the ability to handle temporal dynamics. 4DiM is also used for improved panorama stitching, pose-conditioned video to video translation, and several other tasks. For an overview see https://4d-diffusion.github.io

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at https://github.com/lihenryhfl/pcdm{this https url}.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Large-scale diffusion generative models are greatly simplifying image, video and 3D asset creation from user-provided text prompts and images. However, the challenging problem of text-to-4D dynamic 3D scene generation with diffusion guidance remains largely unexplored. We propose Dream-in-4D, which features a novel two-stage approach for text-to-4D synthesis, leveraging (1) 3D and 2D diffusion guidance to effectively learn a high-quality static 3D asset in the first stage; (2) a deformable neural radiance field that explicitly disentangles the learned static asset from its deformation, preserving quality during motion learning; and (3) a multi-resolution feature grid for the deformation field with a displacement total variation loss to effectively learn motion with video diffusion guidance in the second stage. Through a user preference study, we demonstrate that our approach significantly advances image and motion quality, 3D consistency and text fidelity for text-to-4D generation compared to baseline approaches. Thanks to its motion-disentangled representation, Dream-in-4D can also be easily adapted for controllable generation where appearance is defined by one or multiple images, without the need to modify the motion learning stage. Thus, our method offers, for the first time, a unified approach for text-to-4D, image-to-4D and personalized 4D generation tasks.

Machine-learning datasets labelled "4D" universally denote three spatial dimensions plus time. We introduce HyperShadow, the first public benchmark in which the fourth, fifth, and sixth dimensions are spatial: the task is to decide whether a 3D point cloud is a native three-dimensional shape or the projection, the "shadow", of a rigid object living in R^N (N = 4-6). We show this task is fundamentally distinct from intrinsic-dimension estimation: a shadow is still at-most-3-dimensional data, and standard estimators (TwoNN, Levina-Bickel MLE) reach only 71-73% accuracy. Detection instead requires projection signatures, density folds, filled volumes with characteristic radial profiles, and topology changes, which a 190k-parameter point network recovers at 96.6% accuracy across four corruption tiers, generalizing at 79-91% to object families never seen in training. On a temporal track of rigidly rotating objects we introduce a zero-parameter rigidity witness: the residual of the optimal rigid 3D alignment (Kabsch) between consecutive frames, which must vanish for any rigid 3D motion but cannot vanish for the shadow of a rigid rotation in R^N. This single interpretable statistic separates the classes at AUROC 0.982. All data are generated reproducibly from seeds; the dataset, models, and code are released publicly. HyperShadow makes no claim about physical reality; it is a controlled instrument for studying which observable statistics can certify incompatibility with a purely three-dimensional explanation.

Recently, unsupervised representation learning (URL) has improved the sample efficiency of Reinforcement Learning (RL) by pretraining a model from a large unlabeled dataset. The underlying principle of these methods is to learn temporally predictive representations by predicting future states in the latent space. However, an important challenge of this approach is the representational collapse, where the subspace of the latent representations collapses into a low-dimensional manifold. To address this issue, we propose a novel URL framework that causally predicts future states while increasing the dimension of the latent manifold by decorrelating the features in the latent space. Through extensive empirical studies, we demonstrate that our framework effectively learns predictive representations without collapse, which significantly improves the sample efficiency of state-of-the-art URL methods on the Atari 100k benchmark. The code is available at https://github.com/dojeon-ai/SimTPR.

We present MORPHOS, a novel autoregressive framework that generates dynamic 3D assets from videos across diverse representations, including meshes, 3D Gaussians, and radiance fields. Existing methods are typically limited to a single representation, struggle to model topological changes, or fail to maintain temporal consistency over long videos. To address these limitations, we introduce the Temporal Structured Latents (T-SLAT), a unified 4D representation that jointly encodes geometry and appearance along the temporal dimension. Leveraging T-SLAT, MORPHOS autoregressively generates dynamic 3D assets via causal attention, conditioning each frame on its preceding history to ensure temporal consistency while handling evolving topologies. We also propose a temporal-structural augmentation to mitigate error accumulation in autoregressive generation. MORPHOS achieves state-of-the-art performance in appearance and competitive results in geometry across multiple benchmarks, demonstrating superior generalization across various representations and robustness in long-horizon generation.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Current machine learning models for vision are often highly specialized and limited to a single modality and task. In contrast, recent large language models exhibit a wide range of capabilities, hinting at a possibility for similarly versatile models in computer vision. In this paper, we take a step in this direction and propose a multimodal training scheme called 4M. It consists of training a single unified Transformer encoder-decoder using a masked modeling objective across a wide range of input/output modalities - including text, images, geometric, and semantic modalities, as well as neural network feature maps. 4M achieves scalability by unifying the representation space of all modalities through mapping them into discrete tokens and performing multimodal masked modeling on a small randomized subset of tokens. 4M leads to models that exhibit several key capabilities: (1) they can perform a diverse set of vision tasks out of the box, (2) they excel when fine-tuned for unseen downstream tasks or new input modalities, and (3) they can function as a generative model that can be conditioned on arbitrary modalities, enabling a wide variety of expressive multimodal editing capabilities with remarkable flexibility. Through experimental analyses, we demonstrate the potential of 4M for training versatile and scalable foundation models for vision tasks, setting the stage for further exploration in multimodal learning for vision and other domains.

Recent advances in diffusion models have demonstrated exceptional capabilities in image and video generation, further improving the effectiveness of 4D synthesis. Existing 4D generation methods can generate high-quality 4D objects or scenes based on user-friendly conditions, benefiting the gaming and video industries. However, these methods struggle to synthesize significant object deformation of complex 4D transitions and interactions within scenes. To address this challenge, we propose Trans4D, a novel text-to-4D synthesis framework that enables realistic complex scene transitions. Specifically, we first use multi-modal large language models (MLLMs) to produce a physic-aware scene description for 4D scene initialization and effective transition timing planning. Then we propose a geometry-aware 4D transition network to realize a complex scene-level 4D transition based on the plan, which involves expressive geometrical object deformation. Extensive experiments demonstrate that Trans4D consistently outperforms existing state-of-the-art methods in generating 4D scenes with accurate and high-quality transitions, validating its effectiveness. Code: https://github.com/YangLing0818/Trans4D

Deep latent variable models (DLVMs) are designed to learn meaningful representations in an unsupervised manner, such that the hidden explanatory factors are interpretable by independent latent variables (aka disentanglement). The variational autoencoder (VAE) is a popular DLVM widely studied in disentanglement analysis due to the modeling of the posterior distribution using a factorized Gaussian distribution that encourages the alignment of the latent factors with the latent axes. Several metrics have been proposed recently, assuming that the latent variables explaining the variation in data are aligned with the latent axes (cardinal directions). However, there are other DLVMs, such as the AAE and WAE-MMD (matching the aggregate posterior to the prior), where the latent variables might not be aligned with the latent axes. In this work, we propose a statistical method to evaluate disentanglement for any DLVMs in general. The proposed technique discovers the latent vectors representing the generative factors of a dataset that can be different from the cardinal latent axes. We empirically demonstrate the advantage of the method on two datasets.

With the rapid advancements in diffusion models and 3D generation techniques, dynamic 3D content generation has become a crucial research area. However, achieving high-fidelity 4D (dynamic 3D) generation with strong spatial-temporal consistency remains a challenging task. Inspired by recent findings that pretrained diffusion features capture rich correspondences, we propose FB-4D, a novel 4D generation framework that integrates a Feature Bank mechanism to enhance both spatial and temporal consistency in generated frames. In FB-4D, we store features extracted from previous frames and fuse them into the process of generating subsequent frames, ensuring consistent characteristics across both time and multiple views. To ensure a compact representation, the Feature Bank is updated by a proposed dynamic merging mechanism. Leveraging this Feature Bank, we demonstrate for the first time that generating additional reference sequences through multiple autoregressive iterations can continuously improve generation performance. Experimental results show that FB-4D significantly outperforms existing methods in terms of rendering quality, spatial-temporal consistency, and robustness. It surpasses all multi-view generation tuning-free approaches by a large margin and achieves performance on par with training-based methods.

We present a novel approach for generating high-quality, spatio-temporally coherent human videos from a single image under arbitrary viewpoints. Our framework combines the strengths of U-Nets for accurate condition injection and diffusion transformers for capturing global correlations across viewpoints and time. The core is a cascaded 4D transformer architecture that factorizes attention across views, time, and spatial dimensions, enabling efficient modeling of the 4D space. Precise conditioning is achieved by injecting human identity, camera parameters, and temporal signals into the respective transformers. To train this model, we curate a multi-dimensional dataset spanning images, videos, multi-view data and 3D/4D scans, along with a multi-dimensional training strategy. Our approach overcomes the limitations of previous methods based on GAN or UNet-based diffusion models, which struggle with complex motions and viewpoint changes. Through extensive experiments, we demonstrate our method's ability to synthesize realistic, coherent and free-view human videos, paving the way for advanced multimedia applications in areas such as virtual reality and animation. Our project website is https://human4dit.github.io.

In this paper, we show that the performance of a learnt generative model is closely related to the model's ability to accurately represent the inferred latent data distribution, i.e. its topology and structural properties. We propose LaDDer to achieve accurate modelling of the latent data distribution in a variational autoencoder framework and to facilitate better representation learning. The central idea of LaDDer is a meta-embedding concept, which uses multiple VAE models to learn an embedding of the embeddings, forming a ladder of encodings. We use a non-parametric mixture as the hyper prior for the innermost VAE and learn all the parameters in a unified variational framework. From extensive experiments, we show that our LaDDer model is able to accurately estimate complex latent distribution and results in improvement in the representation quality. We also propose a novel latent space interpolation method that utilises the derived data distribution.

In this paper, we present a novel framework for video-to-4D generation that creates high-quality dynamic 3D content from single video inputs. Direct 4D diffusion modeling is extremely challenging due to costly data construction and the high-dimensional nature of jointly representing 3D shape, appearance, and motion. We address these challenges by introducing a Direct 4DMesh-to-GS Variation Field VAE that directly encodes canonical Gaussian Splats (GS) and their temporal variations from 3D animation data without per-instance fitting, and compresses high-dimensional animations into a compact latent space. Building upon this efficient representation, we train a Gaussian Variation Field diffusion model with temporal-aware Diffusion Transformer conditioned on input videos and canonical GS. Trained on carefully-curated animatable 3D objects from the Objaverse dataset, our model demonstrates superior generation quality compared to existing methods. It also exhibits remarkable generalization to in-the-wild video inputs despite being trained exclusively on synthetic data, paving the way for generating high-quality animated 3D content. Project page: https://gvfdiffusion.github.io/.

Dynamic spatial reasoning from monocular video is essential for bridging visual intelligence and the physical world, yet remains challenging for vision-language models (VLMs). Prior approaches either verbalize spatial-temporal reasoning entirely as text, which is inherently verbose and imprecise for complex dynamics, or rely on external geometric modules that increase inference complexity without fostering intrinsic model capability. In this paper, we present 4DThinker, the first framework that enables VLMs to "think with 4D" through dynamic latent mental imagery, i.e., internally simulating how scenes evolve within the continuous hidden space. Specifically, we first introduce a scalable, annotation-free data generation pipeline that synthesizes 4D reasoning data from raw videos. We then propose Dynamic-Imagery Fine-Tuning (DIFT), which jointly supervises textual tokens and 4D latents to ground the model in dynamic visual semantics. Building on this, 4D Reinforcement Learning (4DRL) further tackles complex reasoning tasks via outcome-based rewards, restricting policy gradients to text tokens to ensure stable optimization. Extensive experiments across multiple dynamic spatial reasoning benchmarks demonstrate that 4DThinker consistently outperforms strong baselines and offers a new perspective toward 4D reasoning in VLMs. Our code is available at https://github.com/zhangquanchen/4DThinker.

While supervised learning has enabled great progress in many applications, unsupervised learning has not seen such widespread adoption, and remains an important and challenging endeavor for artificial intelligence. In this work, we propose a universal unsupervised learning approach to extract useful representations from high-dimensional data, which we call Contrastive Predictive Coding. The key insight of our model is to learn such representations by predicting the future in latent space by using powerful autoregressive models. We use a probabilistic contrastive loss which induces the latent space to capture information that is maximally useful to predict future samples. It also makes the model tractable by using negative sampling. While most prior work has focused on evaluating representations for a particular modality, we demonstrate that our approach is able to learn useful representations achieving strong performance on four distinct domains: speech, images, text and reinforcement learning in 3D environments.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene Structure: Existing methods struggle to reveal the spatial and temporal structure of dynamic scenes from directly learning the complex 6D plenoptic function. (ii) Scaling Deformation Modeling: Explicitly modeling scene element deformation becomes impractical for complex dynamics. To address these issues, we consider the spacetime as an entirety and propose to approximate the underlying spatio-temporal 4D volume of a dynamic scene by optimizing a collection of 4D primitives, with explicit geometry and appearance modeling. Learning to optimize the 4D primitives enables us to synthesize novel views at any desired time with our tailored rendering routine. Our model is conceptually simple, consisting of a 4D Gaussian parameterized by anisotropic ellipses that can rotate arbitrarily in space and time, as well as view-dependent and time-evolved appearance represented by the coefficient of 4D spherindrical harmonics. This approach offers simplicity, flexibility for variable-length video and end-to-end training, and efficient real-time rendering, making it suitable for capturing complex dynamic scene motions. Experiments across various benchmarks, including monocular and multi-view scenarios, demonstrate our 4DGS model's superior visual quality and efficiency.

Vision-language models (VLMs) have demonstrated strong performance in 2D scene understanding and generation, but extending this unification to the physical world remains an open challenge. Existing 3D and 4D approaches typically embed scene geometry into autoregressive model for semantic understanding and diffusion model for content generation. This paradigm gap prevents a single model from jointly handling both tasks, especially in dynamic 4D settings where spatiotemporal modeling is critical. We propose Uni4D-LLM, the first unified VLM framework with spatiotemporal awareness for 4D scene understanding and generation. Our design is guided by two key insights: 1) Unification requires a shared representation. We extract semantic features for understanding and noisy-injected appearance features for generation, incorporate 4D geometric cues, and fuse them into a spatiotemporal-aware visual representation through adaptive cross-attention. 2) Unification requires a shared architecture. Both autoregression and diffusion are built on Transformer backbones, and this enables integration into a single LLM with task-specific heads. By aligning visual and linguistic representations, our Uni4D-LLM produces predictions for both understanding and generation within one Transformer-based framework. We further apply instruction fine-tuning on diverse 4D vision-language datasets to improve generalization across tasks. Extensive experiments on multiple benchmarks demonstrate that Uni4D-LLM achieves competitive or superior results compared to state-of-the-art models and offers the first true unification of 4D scene understanding and generation.

World models have demonstrated significant potential for perceiving and simulating complex environments. Despite their strong performance, the fundamental nature of their learned representations remains poorly understood. In this paper, we investigate the Platonic Representation Hypothesis within this domain by proposing the Predictive Consistency Assumption: we posit that the optimization of a shared state transition objective acts as a selective pressure that encourages heterogeneous models to converge toward a shared latent structure. Through systematic experiments with the DINO World Model (DINO-WM), in which we vary visual encoders to create heterogeneous models, we find that capable world models evolve toward geometrically similar internal structures. Moreover, via model stitching, we show that the internal features of one world model can be mapped to another with limited performance degradation, providing evidence of functional compatibility. Our findings suggest that the pursuit of predictive consistency can promote shared, transition-compatible latent structure across world models.

Flow matching with clean-data prediction has shown that regressing the clean point can exploit low-dimensional structure more effectively than predicting an ambient noised quantity. We ask whether this principle remains useful after images are mapped into a learned latent space, where compression has already removed much of the raw pixel variability. We introduce JLT, a 130M latent diffusion Transformer over frozen FLUX.2 VAE codes, and compare clean-latent prediction with a matched velocity-prediction DiT under the same representation, backbone, and training settings. Although the three variables x, epsilon, and v are linearly convertible for a fixed corruption time, a local Gaussian analysis shows that velocity regression inherits an isotropic target-covariance floor and amplifies low-variance latent directions, while clean prediction damps them. On ImageNet 256 x 256, JLT-B/1 obtains FID-50K 2.50 with classifier-free guidance, with a large matched-target gap over velocity prediction. These results suggest that prediction targets in latent diffusion are representation-dependent geometric choices, rather than interchangeable algebraic parameterizations.

To represent people in mixed reality applications for collaboration and communication, we need to generate realistic and faithful avatar poses. However, the signal streams that can be applied for this task from head-mounted devices (HMDs) are typically limited to head pose and hand pose estimates. While these signals are valuable, they are an incomplete representation of the human body, making it challenging to generate a faithful full-body avatar. We address this challenge by developing a flow-based generative model of the 3D human body from sparse observations, wherein we learn not only a conditional distribution of 3D human pose, but also a probabilistic mapping from observations to the latent space from which we can generate a plausible pose along with uncertainty estimates for the joints. We show that our approach is not only a strong predictive model, but can also act as an efficient pose prior in different optimization settings where a good initial latent code plays a major role.

Auto-regressive models have achieved impressive results in 2D image generation by modeling joint distributions in grid space. In this paper, we extend auto-regressive models to 3D domains, and seek a stronger ability of 3D shape generation by improving auto-regressive models at capacity and scalability simultaneously. Firstly, we leverage an ensemble of publicly available 3D datasets to facilitate the training of large-scale models. It consists of a comprehensive collection of approximately 900,000 objects, with multiple properties of meshes, points, voxels, rendered images, and text captions. This diverse labeled dataset, termed Objaverse-Mix, empowers our model to learn from a wide range of object variations. However, directly applying 3D auto-regression encounters critical challenges of high computational demands on volumetric grids and ambiguous auto-regressive order along grid dimensions, resulting in inferior quality of 3D shapes. To this end, we then present a novel framework Argus3D in terms of capacity. Concretely, our approach introduces discrete representation learning based on a latent vector instead of volumetric grids, which not only reduces computational costs but also preserves essential geometric details by learning the joint distributions in a more tractable order. The capacity of conditional generation can thus be realized by simply concatenating various conditioning inputs to the latent vector, such as point clouds, categories, images, and texts. In addition, thanks to the simplicity of our model architecture, we naturally scale up our approach to a larger model with an impressive 3.6 billion parameters, further enhancing the quality of versatile 3D generation. Extensive experiments on four generation tasks demonstrate that Argus3D can synthesize diverse and faithful shapes across multiple categories, achieving remarkable performance.

As interest grows in world models that predict future states from current observations and actions, accurately modeling part-level dynamics has become increasingly relevant for various applications. Existing approaches, such as Puppet-Master, rely on fine-tuning large-scale pre-trained video diffusion models, which are impractical for real-world use due to the limitations of 2D video representation and slow processing times. To overcome these challenges, we present PartRM, a novel 4D reconstruction framework that simultaneously models appearance, geometry, and part-level motion from multi-view images of a static object. PartRM builds upon large 3D Gaussian reconstruction models, leveraging their extensive knowledge of appearance and geometry in static objects. To address data scarcity in 4D, we introduce the PartDrag-4D dataset, providing multi-view observations of part-level dynamics across over 20,000 states. We enhance the model's understanding of interaction conditions with a multi-scale drag embedding module that captures dynamics at varying granularities. To prevent catastrophic forgetting during fine-tuning, we implement a two-stage training process that focuses sequentially on motion and appearance learning. Experimental results show that PartRM establishes a new state-of-the-art in part-level motion learning and can be applied in manipulation tasks in robotics. Our code, data, and models are publicly available to facilitate future research.

Advances in neural recording present increasing opportunities to study neural activity in unprecedented detail. Latent variable models (LVMs) are promising tools for analyzing this rich activity across diverse neural systems and behaviors, as LVMs do not depend on known relationships between the activity and external experimental variables. However, progress with LVMs for neuronal population activity is currently impeded by a lack of standardization, resulting in methods being developed and compared in an ad hoc manner. To coordinate these modeling efforts, we introduce a benchmark suite for latent variable modeling of neural population activity. We curate four datasets of neural spiking activity from cognitive, sensory, and motor areas to promote models that apply to the wide variety of activity seen across these areas. We identify unsupervised evaluation as a common framework for evaluating models across datasets, and apply several baselines that demonstrate benchmark diversity. We release this benchmark through EvalAI. http://neurallatents.github.io

Joint-embedding predictive architectures (JEPAs) learn latent dynamics for planning and avoid representation collapse by matching features to maximum-entropy distributions such as isotropic Gaussians, yielding dense representations. However, it is unclear whether dense representations are the most favorable geometry for modeling dynamics. In this work, we ask whether a different geometry, sparse representations, can make action-conditioned latent dynamics easier to model, and what dynamical structure emerges from such representations. We first show that nonlinear Lipschitz dynamics can be approximated arbitrarily well by action-conditioned linear dynamics in a sufficiently high-dimensional one-hot latent space, with rollout error vanishing as the dimension grows. This motivates distributed sparse representations as a practical relaxation of one-hot sparsity. We introduce LpWorldModel (LpWM), a JEPA model regularized with Rectified Distribution Matching Regularization (RDMReg) to match encoder features to a Rectified Generalized Gaussian distribution, yielding non-negative sparse codes. Empirically, sparsity lowers the predictor complexity required for successful planning: on PushT, sparse LpWM outperforms dense LeWM by up to 57% in planning success at intermediate predictor capacities. This advantage also extends beyond Gaussian distribution matching, with LpWM outperforming dense VICReg representations across multiple predictor families. We further find that the learned sparse representations are mode-factored, with support encoding discrete dynamical regimes and feature magnitudes capturing continuous within-regime state. Together, these results suggest that sparse representations can reduce the predictor complexity required for control while revealing interpretable structure.

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.

Modeling, understanding, and reconstructing the real world are crucial in XR/VR. Recently, 3D Gaussian Splatting (3D-GS) methods have shown remarkable success in modeling and understanding 3D scenes. Similarly, various 4D representations have demonstrated the ability to capture the dynamics of the 4D world. However, there is a dearth of research focusing on segmentation within 4D representations. In this paper, we propose Segment Any 4D Gaussians (SA4D), one of the first frameworks to segment anything in the 4D digital world based on 4D Gaussians. In SA4D, an efficient temporal identity feature field is introduced to handle Gaussian drifting, with the potential to learn precise identity features from noisy and sparse input. Additionally, a 4D segmentation refinement process is proposed to remove artifacts. Our SA4D achieves precise, high-quality segmentation within seconds in 4D Gaussians and shows the ability to remove, recolor, compose, and render high-quality anything masks. More demos are available at: https://jsxzs.github.io/sa4d/.

We present Free4D, a novel tuning-free framework for 4D scene generation from a single image. Existing methods either focus on object-level generation, making scene-level generation infeasible, or rely on large-scale multi-view video datasets for expensive training, with limited generalization ability due to the scarcity of 4D scene data. In contrast, our key insight is to distill pre-trained foundation models for consistent 4D scene representation, which offers promising advantages such as efficiency and generalizability. 1) To achieve this, we first animate the input image using image-to-video diffusion models followed by 4D geometric structure initialization. 2) To turn this coarse structure into spatial-temporal consistent multiview videos, we design an adaptive guidance mechanism with a point-guided denoising strategy for spatial consistency and a novel latent replacement strategy for temporal coherence. 3) To lift these generated observations into consistent 4D representation, we propose a modulation-based refinement to mitigate inconsistencies while fully leveraging the generated information. The resulting 4D representation enables real-time, controllable rendering, marking a significant advancement in single-image-based 4D scene generation.

Despite advances in Multimodal LLMs (MLLMs), their ability to reason over 3D structures and temporal dynamics remains limited, constrained by weak 4D perception and temporal understanding. Existing 3D and 4D Video Question Answering (VQA) benchmarks also emphasize static scenes and lack region-level prompting. We tackle these issues by introducing: (a) 4D-RGPT, a specialized MLLM designed to capture 4D representations from video inputs with enhanced temporal perception; (b) Perceptual 4D Distillation (P4D), a training framework that transfers 4D representations from a frozen expert model into 4D-RGPT for comprehensive 4D perception; and (c) R4D-Bench, a benchmark for depth-aware dynamic scenes with region-level prompting, built via a hybrid automated and human-verified pipeline. Our 4D-RGPT achieves notable improvements on both existing 4D VQA benchmarks and the proposed R4D-Bench benchmark.

Recent advancements in generative modeling now enable the creation of 4D content (moving 3D objects) controlled with text prompts. 4D generation has large potential in applications like virtual worlds, media, and gaming, but existing methods provide limited control over the appearance and geometry of generated content. In this work, we introduce a method for animating user-provided 3D objects by conditioning on textual prompts to guide 4D generation, enabling custom animations while maintaining the identity of the original object. We first convert a 3D mesh into a ``static" 4D Neural Radiance Field (NeRF) that preserves the visual attributes of the input object. Then, we animate the object using an Image-to-Video diffusion model driven by text. To improve motion realism, we introduce an incremental viewpoint selection protocol for sampling perspectives to promote lifelike movement and a masked Score Distillation Sampling (SDS) loss, which leverages attention maps to focus optimization on relevant regions. We evaluate our model in terms of temporal coherence, prompt adherence, and visual fidelity and find that our method outperforms baselines that are based on other approaches, achieving up to threefold improvements in identity preservation measured using LPIPS scores, and effectively balancing visual quality with dynamic content.

Self-supervised representation learning has shown remarkable success in a number of domains. A common practice is to perform data augmentation via hand-crafted transformations intended to leave the semantics of the data invariant. We seek to understand the empirical success of this approach from a theoretical perspective. We formulate the augmentation process as a latent variable model by postulating a partition of the latent representation into a content component, which is assumed invariant to augmentation, and a style component, which is allowed to change. Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space. We study the identifiability of the latent representation based on pairs of views of the observations and prove sufficient conditions that allow us to identify the invariant content partition up to an invertible mapping in both generative and discriminative settings. We find numerical simulations with dependent latent variables are consistent with our theory. Lastly, we introduce Causal3DIdent, a dataset of high-dimensional, visually complex images with rich causal dependencies, which we use to study the effect of data augmentations performed in practice.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

Generative artificial intelligence (AI) has made significant progress across various domains in recent years. Building on the rapid advancements in 2D, video, and 3D content generation fields, 4D generation has emerged as a novel and rapidly evolving research area, attracting growing attention. 4D generation focuses on creating dynamic 3D assets with spatiotemporal consistency based on user input, offering greater creative freedom and richer immersive experiences. This paper presents a comprehensive survey of the 4D generation field, systematically summarizing its core technologies, developmental trajectory, key challenges, and practical applications, while also exploring potential future research directions. The survey begins by introducing various fundamental 4D representation models, followed by a review of 4D generation frameworks built upon these representations and the key technologies that incorporate motion and geometry priors into 4D assets. We summarize five major challenges of 4D generation: consistency, controllability, diversity, efficiency, and fidelity, accompanied by an outline of existing solutions to address these issues. We systematically analyze applications of 4D generation, spanning dynamic object generation, scene generation, digital human synthesis, 4D editing, and autonomous driving. Finally, we provide an in-depth discussion of the obstacles currently hindering the development of the 4D generation. This survey offers a clear and comprehensive overview of 4D generation, aiming to stimulate further exploration and innovation in this rapidly evolving field. Our code is publicly available at: https://github.com/MiaoQiaowei/Awesome-4D.

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

With the success of 2D and 3D visual generative models, there is growing interest in generating 4D content. Existing methods primarily rely on text prompts to produce 4D content, but they often fall short of accurately defining complex or rare motions. To address this limitation, we propose MagicPose4D, a novel framework for refined control over both appearance and motion in 4D generation. Unlike traditional methods, MagicPose4D accepts monocular videos as motion prompts, enabling precise and customizable motion generation. MagicPose4D comprises two key modules: i) Dual-Phase 4D Reconstruction Module} which operates in two phases. The first phase focuses on capturing the model's shape using accurate 2D supervision and less accurate but geometrically informative 3D pseudo-supervision without imposing skeleton constraints. The second phase refines the model using more accurate pseudo-3D supervision, obtained in the first phase and introduces kinematic chain-based skeleton constraints to ensure physical plausibility. Additionally, we propose a Global-local Chamfer loss that aligns the overall distribution of predicted mesh vertices with the supervision while maintaining part-level alignment without extra annotations. ii) Cross-category Motion Transfer Module} leverages the predictions from the 4D reconstruction module and uses a kinematic-chain-based skeleton to achieve cross-category motion transfer. It ensures smooth transitions between frames through dynamic rigidity, facilitating robust generalization without additional training. Through extensive experiments, we demonstrate that MagicPose4D significantly improves the accuracy and consistency of 4D content generation, outperforming existing methods in various benchmarks.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

In this paper, we propose NeoVerse, a versatile 4D world model that is capable of 4D reconstruction, novel-trajectory video generation, and rich downstream applications. We first identify a common limitation of scalability in current 4D world modeling methods, caused either by expensive and specialized multi-view 4D data or by cumbersome training pre-processing. In contrast, our NeoVerse is built upon a core philosophy that makes the full pipeline scalable to diverse in-the-wild monocular videos. Specifically, NeoVerse features pose-free feed-forward 4D reconstruction, online monocular degradation pattern simulation, and other well-aligned techniques. These designs empower NeoVerse with versatility and generalization to various domains. Meanwhile, NeoVerse achieves state-of-the-art performance in standard reconstruction and generation benchmarks. Our project page is available at https://neoverse-4d.github.io

Joint-Embedding Predictive Architectures (JEPAs) provide a simpleframework for learning world models by predicting future latent representations.However, JEPA training is subject to a bias-variance tradeoff.Without sufficient structural constraints, excessive representationalvariance causes the model to collapse to trivial solutions.The recent LeWorldModel (LeWM) shows that this issue can be alleviated bysimply constraining latent embeddings with an isotropic Gaussian prior.However, latent representations inherently lie on low-dimensional manifoldswithin a high-dimensional ambient space, and enforcing an isotropic Gaussianprior directly in this ambient space introduces an overly strong bias.In this work, we propose ame, which seeks a favorable operatingpoint on the bias-variance frontier by applying Gaussian constraints inmultiple random subspaces rather than in the originalembedding space.This design relaxes the global constraint while preserving itsanti-collapse effect, leading to a better balance between trainingstability and representation flexibility.Extensive experiments across fourcontinuous-control environments demonstrate that consistentlyoutperforms LeWM with very clear margins.Our method is simple yet effective, and serves as a strong baseline for future JEPA-based world model research.fdefinedeeemodeThe code is available at https://github.com/intcomp/Sub-JEPA.

Characterizing the relationship between neural population activity and behavioral data is a central goal of neuroscience. While latent variable models (LVMs) are successful in describing high-dimensional time-series data, they are typically only designed for a single type of data, making it difficult to identify structure shared across different experimental data modalities. Here, we address this shortcoming by proposing an unsupervised LVM which extracts temporally evolving shared and independent latents for distinct, simultaneously recorded experimental modalities. We do this by combining Gaussian Process Factor Analysis (GPFA), an interpretable LVM for neural spiking data with temporally smooth latent space, with Gaussian Process Variational Autoencoders (GP-VAEs), which similarly use a GP prior to characterize correlations in a latent space, but admit rich expressivity due to a deep neural network mapping to observations. We achieve interpretability in our model by partitioning latent variability into components that are either shared between or independent to each modality. We parameterize the latents of our model in the Fourier domain, and show improved latent identification using this approach over standard GP-VAE methods. We validate our model on simulated multi-modal data consisting of Poisson spike counts and MNIST images that scale and rotate smoothly over time. We show that the multi-modal GP-VAE (MM-GPVAE) is able to not only identify the shared and independent latent structure across modalities accurately, but provides good reconstructions of both images and neural rates on held-out trials. Finally, we demonstrate our framework on two real world multi-modal experimental settings: Drosophila whole-brain calcium imaging alongside tracked limb positions, and Manduca sexta spike train measurements from ten wing muscles as the animal tracks a visual stimulus.

Recent progress has been made towards learning invariant or equivariant representations with self-supervised learning. While invariant methods are evaluated on large scale datasets, equivariant ones are evaluated in smaller, more controlled, settings. We aim at bridging the gap between the two in order to learn more diverse representations that are suitable for a wide range of tasks. We start by introducing a dataset called 3DIEBench, consisting of renderings from 3D models over 55 classes and more than 2.5 million images where we have full control on the transformations applied to the objects. We further introduce a predictor architecture based on hypernetworks to learn equivariant representations with no possible collapse to invariance. We introduce SIE (Split Invariant-Equivariant) which combines the hypernetwork-based predictor with representations split in two parts, one invariant, the other equivariant, to learn richer representations. We demonstrate significant performance gains over existing methods on equivariance related tasks from both a qualitative and quantitative point of view. We further analyze our introduced predictor and show how it steers the learned latent space. We hope that both our introduced dataset and approach will enable learning richer representations without supervision in more complex scenarios. Code and data are available at https://github.com/facebookresearch/SIE.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Recent breakthroughs in text-to-4D generation rely on pre-trained text-to-image and text-to-video models to generate dynamic 3D scenes. However, current text-to-4D methods face a three-way tradeoff between the quality of scene appearance, 3D structure, and motion. For example, text-to-image models and their 3D-aware variants are trained on internet-scale image datasets and can be used to produce scenes with realistic appearance and 3D structure -- but no motion. Text-to-video models are trained on relatively smaller video datasets and can produce scenes with motion, but poorer appearance and 3D structure. While these models have complementary strengths, they also have opposing weaknesses, making it difficult to combine them in a way that alleviates this three-way tradeoff. Here, we introduce hybrid score distillation sampling, an alternating optimization procedure that blends supervision signals from multiple pre-trained diffusion models and incorporates benefits of each for high-fidelity text-to-4D generation. Using hybrid SDS, we demonstrate synthesis of 4D scenes with compelling appearance, 3D structure, and motion.

Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer from a coherence-quality tradeoff, where models with good generation quality lack generative coherence across modalities, and vice versa. We discuss the limitations underlying the unsatisfactory performance of existing methods, to motivate the need for a different approach. We propose a novel method that uses a set of independently trained, uni-modal, deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is fed to a masked diffusion model to enable generative modeling. We also introduce a new multi-time training method to learn the conditional score network for multi-modal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign.

We present a latent diffusion model over 3D scenes, that can be trained using only 2D image data. To achieve this, we first design an autoencoder that maps multi-view images to 3D Gaussian splats, and simultaneously builds a compressed latent representation of these splats. Then, we train a multi-view diffusion model over the latent space to learn an efficient generative model. This pipeline does not require object masks nor depths, and is suitable for complex scenes with arbitrary camera positions. We conduct careful experiments on two large-scale datasets of complex real-world scenes -- MVImgNet and RealEstate10K. We show that our approach enables generating 3D scenes in as little as 0.2 seconds, either from scratch, from a single input view, or from sparse input views. It produces diverse and high-quality results while running an order of magnitude faster than non-latent diffusion models and earlier NeRF-based generative models

We present Stable Video 4D (SV4D), a latent video diffusion model for multi-frame and multi-view consistent dynamic 3D content generation. Unlike previous methods that rely on separately trained generative models for video generation and novel view synthesis, we design a unified diffusion model to generate novel view videos of dynamic 3D objects. Specifically, given a monocular reference video, SV4D generates novel views for each video frame that are temporally consistent. We then use the generated novel view videos to optimize an implicit 4D representation (dynamic NeRF) efficiently, without the need for cumbersome SDS-based optimization used in most prior works. To train our unified novel view video generation model, we curated a dynamic 3D object dataset from the existing Objaverse dataset. Extensive experimental results on multiple datasets and user studies demonstrate SV4D's state-of-the-art performance on novel-view video synthesis as well as 4D generation compared to prior works.

Recently, multi-view or 4D video generation has emerged as a significant research topic. Nonetheless, recent approaches to 4D generation still struggle with fundamental limitations, as they primarily rely on harnessing multiple video diffusion models with additional training or compute-intensive training of a full 4D diffusion model with limited real-world 4D data and large computational costs. To address these challenges, here we propose the first training-free 4D video generation method that leverages the off-the-shelf video diffusion models to generate multi-view videos from a single input video. Our approach consists of two key steps: (1) By designating the edge frames in the spatio-temporal sampling grid as key frames, we first synthesize them using a video diffusion model, leveraging a depth-based warping technique for guidance. This approach ensures structural consistency across the generated frames, preserving spatial and temporal coherence. (2) We then interpolate the remaining frames using a video diffusion model, constructing a fully populated and temporally coherent sampling grid while preserving spatial and temporal consistency. Through this approach, we extend a single video into a multi-view video along novel camera trajectories while maintaining spatio-temporal consistency. Our method is training-free and fully utilizes an off-the-shelf video diffusion model, offering a practical and effective solution for multi-view video generation.

Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance.

Understanding dynamic outdoor environments requires capturing complex object interactions and their evolution over time. LiDAR-based 4D point clouds provide precise spatial geometry and rich temporal cues, making them ideal for representing real-world scenes. However, despite their potential, 4D LiDAR remains underexplored in the context of Multimodal Large Language Models (MLLMs) due to the absence of high-quality, modality-specific annotations and the lack of MLLM architectures capable of processing its high-dimensional composition. To address these challenges, we introduce B4DL, a new benchmark specifically designed for training and evaluating MLLMs on 4D LiDAR understanding. In addition, we propose a scalable data generation pipeline and an MLLM model that, for the first time, directly processes raw 4D LiDAR by bridging it with language understanding. Combined with our dataset and benchmark, our model offers a unified solution for spatio-temporal reasoning in dynamic outdoor environments. We provide rendered 4D LiDAR videos, generated dataset, and inference outputs on diverse scenarios at: https://github.com/ccho4702/B4DL

Extracting dynamic 4D object interactions from massive, in-the-wild monocular videos offers a highly efficient data collection pathway for scaling Embodied AI and training VLAs. However, existing monocular 4D reconstruction methods primarily focus on isolated objects, often failing under the severe occlusions and complex dynamics inherent in multi-object interactions. To bridge this gap, we propose HAT-4D, the first agentic framework designed to reconstruct the 3D geometry, temporal dynamics, and physical interactions of multiple objects from a single video. By integrating VLMs with a multi-level human-in-the-loop feedback mechanism, HAT-4D efficiently resolves depth ambiguities and interaction-induced occlusions during 3D generation and 4D propagation, yielding physically plausible assets without relying on expensive multicamera rigs. As a scalable data engine, HAT-4D facilitates the creation of MVOIK-4D, an open-world benchmark for monocular 4D interaction reconstruction, accompanied by a novel multi-dimensional evaluation protocol focused on physical plausibility and temporal consistency. Extensive experiments demonstrate that HAT-4D achieves SOTA performance on most evaluation metrics, while maintaining competitive semantic alignment. Ablation studies show that introducing a small amount of human feedback improves interaction reconstruction. Moreover, the data produced by HAT-4D effectively improves baseline performance when used for fine-tuning. Our data and code are available at https://lijiaxin0111.github.io/HAT4D/

In image generation, Multiple Latent Variable Generative Models (MLVGMs) employ multiple latent variables to gradually shape the final images, from global characteristics to finer and local details (e.g., StyleGAN, NVAE), emerging as powerful tools for diverse applications. Yet their generative dynamics remain only empirically observed, without a systematic understanding of each latent variable's impact. In this work, we propose a novel framework that quantifies the contribution of each latent variable using Mutual Information (MI) as a metric. Our analysis reveals that current MLVGMs often underutilize some latent variables, and provides actionable insights for their use in downstream applications. With this foundation, we introduce a method for generating synthetic data for Self-Supervised Contrastive Representation Learning (SSCRL). By leveraging the hierarchical and disentangled variables of MLVGMs, our approach produces diverse and semantically meaningful views without the need for real image data. Additionally, we introduce a Continuous Sampling (CS) strategy, where the generator dynamically creates new samples during SSCRL training, greatly increasing data variability. Our comprehensive experiments demonstrate the effectiveness of these contributions, showing that MLVGMs' generated views compete on par with or even surpass views generated from real data. This work establishes a principled approach to understanding and exploiting MLVGMs, advancing both generative modeling and self-supervised learning. Code and pre-trained models at: https://github.com/SerezD/mi_ml_gen.

In recent years, the increasing demand for dynamic 3D assets in design and gaming applications has given rise to powerful generative pipelines capable of synthesizing high-quality 4D objects. Previous methods generally rely on score distillation sampling (SDS) algorithm to infer the unseen views and motion of 4D objects, thus leading to unsatisfactory results with defects like over-saturation and Janus problem. Therefore, inspired by recent progress of video diffusion models, we propose to optimize a 4D representation by explicitly generating multi-view videos from one input image. However, it is far from trivial to handle practical challenges faced by such a pipeline, including dramatic temporal inconsistency, inter-frame geometry and texture diversity, and semantic defects brought by video generation results. To address these issues, we propose DG4D, a novel multi-stage framework that generates high-quality and consistent 4D assets without score distillation. Specifically, collaborative techniques and solutions are developed, including an attention injection strategy to synthesize temporal-consistent multi-view videos, a robust and efficient dynamic reconstruction method based on Gaussian Splatting, and a refinement stage with diffusion prior for semantic restoration. The qualitative results and user preference study demonstrate that our framework outperforms the baselines in generation quality by a considerable margin. Code will be released at https://github.com/jasongzy/EG4D.

Recent advances in diffusion models have revolutionized 2D and 3D content creation, yet generating photorealistic dynamic 4D scenes remains a significant challenge. Existing dynamic 4D generation methods typically rely on distilling knowledge from pre-trained 3D generative models, often fine-tuned on synthetic object datasets. Consequently, the resulting scenes tend to be object-centric and lack photorealism. While text-to-video models can generate more realistic scenes with motion, they often struggle with spatial understanding and provide limited control over camera viewpoints during rendering. To address these limitations, we present PaintScene4D, a novel text-to-4D scene generation framework that departs from conventional multi-view generative models in favor of a streamlined architecture that harnesses video generative models trained on diverse real-world datasets. Our method first generates a reference video using a video generation model, and then employs a strategic camera array selection for rendering. We apply a progressive warping and inpainting technique to ensure both spatial and temporal consistency across multiple viewpoints. Finally, we optimize multi-view images using a dynamic renderer, enabling flexible camera control based on user preferences. Adopting a training-free architecture, our PaintScene4D efficiently produces realistic 4D scenes that can be viewed from arbitrary trajectories. The code will be made publicly available. Our project page is at https://paintscene4d.github.io/

In this paper, we present Consistent4D, a novel approach for generating 4D dynamic objects from uncalibrated monocular videos. Uniquely, we cast the 360-degree dynamic object reconstruction as a 4D generation problem, eliminating the need for tedious multi-view data collection and camera calibration. This is achieved by leveraging the object-level 3D-aware image diffusion model as the primary supervision signal for training Dynamic Neural Radiance Fields (DyNeRF). Specifically, we propose a Cascade DyNeRF to facilitate stable convergence and temporal continuity under the supervision signal which is discrete along the time axis. To achieve spatial and temporal consistency, we further introduce an Interpolation-driven Consistency Loss. It is optimized by minimizing the discrepancy between rendered frames from DyNeRF and interpolated frames from a pre-trained video interpolation model. Extensive experiments show that our Consistent4D can perform competitively to prior art alternatives, opening up new possibilities for 4D dynamic object generation from monocular videos, whilst also demonstrating advantage for conventional text-to-3D generation tasks. Our project page is https://consistent4d.github.io/.

This paper proposes a new type of generative model that is able to quickly learn a latent representation without an encoder. This is achieved using empirical Bayes to calculate the expectation of the posterior, which is implemented by initialising a latent vector with zeros, then using the gradient of the log-likelihood of the data with respect to this zero vector as new latent points. The approach has similar characteristics to autoencoders, but with a simpler architecture, and is demonstrated in a variational autoencoder equivalent that permits sampling. This also allows implicit representation networks to learn a space of implicit functions without requiring a hypernetwork, retaining their representation advantages across datasets. The experiments show that the proposed method converges faster, with significantly lower reconstruction error than autoencoders, while requiring half the parameters.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Latent diffusion models (LDMs) have recently achieved strong performance in 3D medical image synthesis. However, modalities like cine cardiac MRI (CMR), representing a temporally synchronized 3D volume across the cardiac cycle, add an additional dimension that most generative approaches do not model directly. Instead, they factorize space and time or enforce temporal consistency through auxiliary mechanisms such as anatomical masks. Such strategies introduce structural biases that may limit global context integration and lead to subtle spatiotemporal discontinuities or physiologically inconsistent cardiac dynamics. We investigate whether a unified 4D generative model can learn continuous cardiac dynamics without architectural factorization. We propose CardioDiT, a fully 4D latent diffusion framework for short-axis cine CMR synthesis based on diffusion transformers. A spatiotemporal VQ-VAE encodes 2D+t slices into compact latents, which a diffusion transformer then models jointly as complete 3D+t volumes, coupling space and time throughout the generative process. We evaluate CardioDiT on public CMR datasets and a larger private cohort, comparing it to baselines with progressively stronger spatiotemporal coupling. Results show improved inter-slice consistency, temporally coherent motion, and realistic cardiac function distributions, suggesting that explicit 4D modeling with a diffusion transformer provides a principled foundation for spatiotemporal cardiac image synthesis. Code and models trained on public data are available at https://github.com/Cardio-AI/cardiodit.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Multimodal Large Language Models (MLLMs) have demonstrated impressive 2D image/video understanding capabilities. However, there are no publicly standardized benchmarks to assess the abilities of MLLMs in understanding the 4D objects (3D objects with temporal evolution over time). In this paper, we introduce 4D-Bench, the first benchmark to evaluate the capabilities of MLLMs in 4D object understanding, featuring tasks in 4D object Question Answering (4D object QA) and 4D object captioning. 4D-Bench provides 4D objects with diverse categories, high-quality annotations, and tasks necessitating multi-view spatial-temporal understanding, different from existing 2D image/video-based benchmarks. With 4D-Bench, we evaluate a wide range of open-source and closed-source MLLMs. The results from the 4D object captioning experiment indicate that MLLMs generally exhibit weaker temporal understanding compared to their appearance understanding, notably, while open-source models approach closed-source performance in appearance understanding, they show larger performance gaps in temporal understanding. 4D object QA yields surprising findings: even with simple single-object videos, MLLMs perform poorly, with state-of-the-art GPT-4o achieving only 63\% accuracy compared to the human baseline of 91\%. These findings highlight a substantial gap in 4D object understanding and the need for further advancements in MLLMs.

4D content generation focuses on creating dynamic 3D objects that change over time. Existing methods primarily rely on pre-trained video diffusion models, utilizing sampling processes or reference videos. However, these approaches face significant challenges. Firstly, the generated 4D content often fails to adhere to real-world physics since video diffusion models do not incorporate physical priors. Secondly, the extensive sampling process and the large number of parameters in diffusion models result in exceedingly time-consuming generation processes. To address these issues, we introduce Phy124, a novel, fast, and physics-driven method for controllable 4D content generation from a single image. Phy124 integrates physical simulation directly into the 4D generation process, ensuring that the resulting 4D content adheres to natural physical laws. Phy124 also eliminates the use of diffusion models during the 4D dynamics generation phase, significantly speeding up the process. Phy124 allows for the control of 4D dynamics, including movement speed and direction, by manipulating external forces. Extensive experiments demonstrate that Phy124 generates high-fidelity 4D content with significantly reduced inference times, achieving stateof-the-art performance. The code and generated 4D content are available at the provided link: https://anonymous.4open.science/r/BBF2/.

Latent-based image generative models, such as Latent Diffusion Models (LDMs) and Mask Image Models (MIMs), have achieved notable success in image generation tasks. These models typically leverage reconstructive autoencoders like VQGAN or VAE to encode pixels into a more compact latent space and learn the data distribution in the latent space instead of directly from pixels. However, this practice raises a pertinent question: Is it truly the optimal choice? In response, we begin with an intriguing observation: despite sharing the same latent space, autoregressive models significantly lag behind LDMs and MIMs in image generation. This finding contrasts sharply with the field of NLP, where the autoregressive model GPT has established a commanding presence. To address this discrepancy, we introduce a unified perspective on the relationship between latent space and generative models, emphasizing the stability of latent space in image generative modeling. Furthermore, we propose a simple but effective discrete image tokenizer to stabilize the latent space for image generative modeling. Experimental results show that image autoregressive modeling with our tokenizer (DiGIT) benefits both image understanding and image generation with the next token prediction principle, which is inherently straightforward for GPT models but challenging for other generative models. Remarkably, for the first time, a GPT-style autoregressive model for images outperforms LDMs, which also exhibits substantial improvement akin to GPT when scaling up model size. Our findings underscore the potential of an optimized latent space and the integration of discrete tokenization in advancing the capabilities of image generative models. The code is available at https://github.com/DAMO-NLP-SG/DiGIT.

Recent progress in latent world models (e.g., V-JEPA2) has shown promising capability in forecasting future world states from video observations. Nevertheless, dense prediction from a short observation window limits temporal context and can bias predictors toward local, low-level extrapolation, making it difficult to capture long-horizon semantics and reducing downstream utility. Vision--language models (VLMs), in contrast, provide strong semantic grounding and general knowledge by reasoning over uniformly sampled frames, but they are not ideal as standalone dense predictors due to compute-driven sparse sampling, a language-output bottleneck that compresses fine-grained interaction states into text-oriented representations, and a data-regime mismatch when adapting to small action-conditioned datasets. We propose a VLM-guided JEPA-style latent world modeling framework that combines dense-frame dynamics modeling with long-horizon semantic guidance via a dual-temporal pathway: a dense JEPA branch for fine-grained motion and interaction cues, and a uniformly sampled VLM thinker branch with a larger temporal stride for knowledge-rich guidance. To transfer the VLM's progressive reasoning signals effectively, we introduce a hierarchical pyramid representation extraction module that aggregates multi-layer VLM representations into guidance features compatible with latent prediction. Experiments on hand-manipulation trajectory prediction show that our method outperforms both a strong VLM-only baseline and a JEPA-predictor baseline, and yields more robust long-horizon rollout behavior.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via the 1-Wasserstein distance, using only paired data. This two-step approach minimizes an upper bound on the 1-Wasserstein distance between joint distributions, reducing reliance on scarce paired samples while enabling fast one-step generation. Theoretically, we establish non-asymptotic error bounds and demonstrate a key benefit of unpaired data: enhanced geometric fidelity in generated outputs. Furthermore, by extending the scope of its two core steps, LSDM provides a coherent statistical perspective that connects to a broad class of latent-space approaches. Notably, Latent Diffusion Models (LDMs) can be viewed as a variant of LSDM, in which joint distribution matching is achieved indirectly via score matching. Consequently, our results also provide theoretical insights into the consistency of LDMs. Empirical evaluations on real-world image tasks, including class-conditional generation and image super-resolution, demonstrate the effectiveness of LSDM in leveraging unpaired data to enhance generation quality.

We propose CARFF: Conditional Auto-encoded Radiance Field for 3D Scene Forecasting, a method for predicting future 3D scenes given past observations, such as 2D ego-centric images. Our method maps an image to a distribution over plausible 3D latent scene configurations using a probabilistic encoder, and predicts the evolution of the hypothesized scenes through time. Our latent scene representation conditions a global Neural Radiance Field (NeRF) to represent a 3D scene model, which enables explainable predictions and straightforward downstream applications. This approach extends beyond previous neural rendering work by considering complex scenarios of uncertainty in environmental states and dynamics. We employ a two-stage training of Pose-Conditional-VAE and NeRF to learn 3D representations. Additionally, we auto-regressively predict latent scene representations as a partially observable Markov decision process, utilizing a mixture density network. We demonstrate the utility of our method in realistic scenarios using the CARLA driving simulator, where CARFF can be used to enable efficient trajectory and contingency planning in complex multi-agent autonomous driving scenarios involving visual occlusions.

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

This paper aims to deal with the ignored real-world complexities in prior work on human motion forecasting, emphasizing the social properties of multi-person motion, the diversity of motion and social interactions, and the complexity of articulated motion. To this end, we introduce a novel task of stochastic multi-person 3D motion forecasting. We propose a dual-level generative modeling framework that separately models independent individual motion at the local level and social interactions at the global level. Notably, this dual-level modeling mechanism can be achieved within a shared generative model, through introducing learnable latent codes that represent intents of future motion and switching the codes' modes of operation at different levels. Our framework is general; we instantiate it with different generative models, including generative adversarial networks and diffusion models, and various multi-person forecasting models. Extensive experiments on CMU-Mocap, MuPoTS-3D, and SoMoF benchmarks show that our approach produces diverse and accurate multi-person predictions, significantly outperforming the state of the art.

Recent advances in 4D generation mainly focus on generating 4D content by distilling pre-trained text or single-view image-conditioned models. It is inconvenient for them to take advantage of various off-the-shelf 3D assets with multi-view attributes, and their results suffer from spatiotemporal inconsistency owing to the inherent ambiguity in the supervision signals. In this work, we present Animate3D, a novel framework for animating any static 3D model. The core idea is two-fold: 1) We propose a novel multi-view video diffusion model (MV-VDM) conditioned on multi-view renderings of the static 3D object, which is trained on our presented large-scale multi-view video dataset (MV-Video). 2) Based on MV-VDM, we introduce a framework combining reconstruction and 4D Score Distillation Sampling (4D-SDS) to leverage the multi-view video diffusion priors for animating 3D objects. Specifically, for MV-VDM, we design a new spatiotemporal attention module to enhance spatial and temporal consistency by integrating 3D and video diffusion models. Additionally, we leverage the static 3D model's multi-view renderings as conditions to preserve its identity. For animating 3D models, an effective two-stage pipeline is proposed: we first reconstruct motions directly from generated multi-view videos, followed by the introduced 4D-SDS to refine both appearance and motion. Qualitative and quantitative experiments demonstrate that Animate3D significantly outperforms previous approaches. Data, code, and models will be open-released.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

This paper presents an effective approach for learning novel 4D embodied world models, which predict the dynamic evolution of 3D scenes over time in response to an embodied agent's actions, providing both spatial and temporal consistency. We propose to learn a 4D world model by training on RGB-DN (RGB, Depth, and Normal) videos. This not only surpasses traditional 2D models by incorporating detailed shape, configuration, and temporal changes into their predictions, but also allows us to effectively learn accurate inverse dynamic models for an embodied agent. Specifically, we first extend existing robotic manipulation video datasets with depth and normal information leveraging off-the-shelf models. Next, we fine-tune a video generation model on this annotated dataset, which jointly predicts RGB-DN (RGB, Depth, and Normal) for each frame. We then present an algorithm to directly convert generated RGB, Depth, and Normal videos into a high-quality 4D scene of the world. Our method ensures temporal and spatial coherence in 4D scene predictions from embodied scenarios, enables novel view synthesis for embodied environments, and facilitates policy learning that significantly outperforms those derived from prior video-based world models.

Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering. Implementation is available at https://github.com/eladrich/latent-nerf

Recent AI-based 3D content creation has largely evolved along two paths: feed-forward image-to-3D reconstruction approaches and 3D generative models trained with 2D or 3D supervision. In this work, we show that existing feed-forward reconstruction methods can serve as effective latent encoders for training 3D generative models, thereby bridging these two paradigms. By reusing powerful pre-trained reconstruction models, we avoid computationally expensive encoder network training and obtain rich 3D latent features for generative modeling for free. However, the latent spaces of reconstruction models are not well-suited for generative modeling due to their unstructured nature. To enable flow-based model training on these latent features, we develop post-processing pipelines, including protocols to standardize the features and spatial weighting to concentrate on important regions. We further incorporate a 2D image space perceptual rendering loss to handle the high-dimensional latent spaces. Finally, we propose a multi-stream transformer-based rectified flow architecture to achieve linear scaling and high-quality text-conditioned 3D generation. Our framework leverages the advancements of feed-forward reconstruction models to enhance the scalability of 3D generative modeling, achieving both high computational efficiency and state-of-the-art performance in text-to-3D generation.

Recent developments in 2D visual generation have been remarkably successful. However, 3D and 4D generation remain challenging in real-world applications due to the lack of large-scale 4D data and effective model design. In this paper, we propose to jointly investigate general 3D and 4D generation by leveraging camera and object movements commonly observed in daily life. Due to the lack of real-world 4D data in the community, we first propose a data curation pipeline to obtain camera poses and object motion strength from videos. Based on this pipeline, we introduce a large-scale real-world 4D scene dataset: CamVid-30K. By leveraging all the 3D and 4D data, we develop our framework, GenXD, which allows us to produce any 3D or 4D scene. We propose multiview-temporal modules, which disentangle camera and object movements, to seamlessly learn from both 3D and 4D data. Additionally, GenXD employs masked latent conditions to support a variety of conditioning views. GenXD can generate videos that follow the camera trajectory as well as consistent 3D views that can be lifted into 3D representations. We perform extensive evaluations across various real-world and synthetic datasets, demonstrating GenXD's effectiveness and versatility compared to previous methods in 3D and 4D generation.

Simulating robot-world interactions is a cornerstone of Embodied AI. Recently, a few works have shown promise in leveraging video generations to transcend the rigid visual/physical constraints of traditional simulators. However, they primarily operate in 2D space or are guided by static environmental cues, ignoring the fundamental reality that robot-world interactions are inherently 4D spatiotemporal events that require precise interactive modeling. To restore this 4D essence while ensuring the precise robot control, we introduce Kinema4D, a new action-conditioned 4D generative robotic simulator that disentangles the robot-world interaction into: i) Precise 4D representation of robot controls: we drive a URDF-based 3D robot via kinematics, producing a precise 4D robot control trajectory. ii) Generative 4D modeling of environmental reactions: we project the 4D robot trajectory into a pointmap as a spatiotemporal visual signal, controlling the generative model to synthesize complex environments' reactive dynamics into synchronized RGB/pointmap sequences. To facilitate training, we curated a large-scale dataset called Robo4D-200k, comprising 201,426 robot interaction episodes with high-quality 4D annotations. Extensive experiments demonstrate that our method effectively simulates physically-plausible, geometry-consistent, and embodiment-agnostic interactions that faithfully mirror diverse real-world dynamics. For the first time, it shows potential zero-shot transfer capability, providing a high-fidelity foundation for advancing next-generation embodied simulation.

Document clustering and topic modeling are two closely related tasks which can mutually benefit each other. Topic modeling can project documents into a topic space which facilitates effective document clustering. Cluster labels discovered by document clustering can be incorporated into topic models to extract local topics specific to each cluster and global topics shared by all clusters. In this paper, we propose a multi-grain clustering topic model (MGCTM) which integrates document clustering and topic modeling into a unified framework and jointly performs the two tasks to achieve the overall best performance. Our model tightly couples two components: a mixture component used for discovering latent groups in document collection and a topic model component used for mining multi-grain topics including local topics specific to each cluster and global topics shared across clusters.We employ variational inference to approximate the posterior of hidden variables and learn model parameters. Experiments on two datasets demonstrate the effectiveness of our model.

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used throughout the book and serve at a reminder of basic concepts in calculus, linear algebra and probability and also introduces some measure theoretic terminology, which can be used as a reading guide for the sections that use these tools. The introductory chapters also provide background material on matrix analysis and optimization. The latter chapter provides theoretical support to many algorithms that are used in the book, including stochastic gradient descent, proximal methods, etc. After discussing basic concepts for statistical prediction, the book includes an introduction to reproducing kernel theory and Hilbert space techniques, which are used in many places, before addressing the description of various algorithms for supervised statistical learning, including linear methods, support vector machines, decision trees, boosting, or neural networks. The subject then switches to generative methods, starting with a chapter that presents sampling methods and an introduction to the theory of Markov chains. The following chapter describe the theory of graphical models, an introduction to variational methods for models with latent variables, and to deep-learning based generative models. The next chapters focus on unsupervised learning methods, for clustering, factor analysis and manifold learning. The final chapter of the book is theory-oriented and discusses concentration inequalities and generalization bounds.

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for producing new realizations from a limited set of available runs by transferring structure learned across an ensemble. Using monthly near-surface temperature time series from ten independent reanalysis realizations (ERA5), we find that a vanilla conditional variational autoencoder (CVAE) trained jointly across realizations yields a fragmented latent space that fails to generalize to unseen ensemble members. To address this, we introduce a latent-constrained CVAE (LC-CVAE) that enforces cross-realization homogeneity of latent embeddings at a small set of shared geographic 'anchor' locations. We then use multi-output Gaussian process regression in the latent space to predict latent coordinates at unsampled locations in a new realization, followed by decoding to generate full time series fields. Experiments and ablations demonstrate (i) instability when training on a single realization, (ii) diminishing returns after incorporating roughly five realizations, and (iii) a trade-off between spatial coverage and reconstruction quality that is closely linked to the average neighbor distance in latent space.

Recent Text-to-Video (T2V) models have demonstrated powerful capability in visual simulation of real-world geometry and physical laws, indicating its potential as implicit world models. Inspired by this, we explore the feasibility of leveraging the video generation prior for viewpoint planning from given 4D scenes, since videos internally accompany dynamic scenes with natural viewpoints. To this end, we propose a two-stage paradigm to adapt pre-trained T2V models for viewpoint prediction, in a compatible manner. First, we inject the 4D scene representation into the pre-trained T2V model via an adaptive learning branch, where the 4D scene is viewpoint-agnostic and the conditional generated video embeds the viewpoints visually. Then, we formulate viewpoint extraction as a hybrid-condition guided camera extrinsic denoising process. Specifically, a camera extrinsic diffusion branch is further introduced onto the pre-trained T2V model, by taking the generated video and 4D scene as input. Experimental results show the superiority of our proposed method over existing competitors, and ablation studies validate the effectiveness of our key technical designs. To some extent, this work proves the potential of video generation models toward 4D interaction in real world.

Text-guided diffusion models have revolutionized image and video generation and have also been successfully used for optimization-based 3D object synthesis. Here, we instead focus on the underexplored text-to-4D setting and synthesize dynamic, animated 3D objects using score distillation methods with an additional temporal dimension. Compared to previous work, we pursue a novel compositional generation-based approach, and combine text-to-image, text-to-video, and 3D-aware multiview diffusion models to provide feedback during 4D object optimization, thereby simultaneously enforcing temporal consistency, high-quality visual appearance and realistic geometry. Our method, called Align Your Gaussians (AYG), leverages dynamic 3D Gaussian Splatting with deformation fields as 4D representation. Crucial to AYG is a novel method to regularize the distribution of the moving 3D Gaussians and thereby stabilize the optimization and induce motion. We also propose a motion amplification mechanism as well as a new autoregressive synthesis scheme to generate and combine multiple 4D sequences for longer generation. These techniques allow us to synthesize vivid dynamic scenes, outperform previous work qualitatively and quantitatively and achieve state-of-the-art text-to-4D performance. Due to the Gaussian 4D representation, different 4D animations can be seamlessly combined, as we demonstrate. AYG opens up promising avenues for animation, simulation and digital content creation as well as synthetic data generation.