VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos

Learning a physical model from video data that can comprehend physical laws and predict the future trajectories of objects is a formidable challenge in artificial intelligence. Prior approaches either leverage various Partial Differential Equations (PDEs) as soft constraints in the form of PINN losses, or integrate physics simulators into neural networks; however, they often rely on strong priors or high-quality geometry reconstruction. In this paper, we propose CausalGS, a framework that learns the causal dynamics of complex dynamic 3D scenes solely from multi-view videos, while dispensing with the reliance on explicit priors. At its core is an inverse physics inference module that decouples the complex dynamics problem from the video into the joint inference of two factors: the initial velocity field representing the scene's kinematics, and the intrinsic material properties governing its dynamics. This inferred physical information is then utilized within a differentiable physics simulator to guide the learning process in a physics-regularized manner. Extensive experiments demonstrate that CausalGS surpasses the state-of-the-art on the highly challenging task of long-term future frame extrapolation, while also exhibiting advanced performance in novel view interpolation. Crucially, our work shows that, without any human annotation, the model is able to learn the complex interactions between multiple physical properties and understand the causal relationships driving the scene's dynamic evolution, solely from visual observations.

We present a self-supervised framework for learning implicit 3D physical dynamics directly from video-derived supervisory signals. While current generative video models achieve high visual fidelity, they lack a 3D geometric foundation, often resulting in physical inconsistencies and a failure to maintain object permanence. We address this by shifting the predictive bottleneck from 2D image space to a `lifted' 3D Volumetric Latent Space. Our method unprojects semantic features from a Video Joint-Embedding Predictive Architecture (V-JEPA) into a voxelized grid, grounded by monocular depth priors. This lifting enables a Volumetric Feature Advection to learn an action-conditioned transition operator that treats physics as a spatio-temporal state advection problem, i.e., learn implicit 3D physics. Unlike state-of-the-art hybrid models that rely on explicit classical simulators for training and/or inference, our architecture tracks material states implicitly within high-dimensional V-JEPA features. This allows for the emergent simulation of heterogeneous phenomena (e.g., rigid body motion in fluid flow) within a single, unified pipeline. Supervised solely via end-to-end video-derived signal plus action conditions, without access to physics engine internal states, labels, or surrogate models, our model demonstrates good long-term structural stability and physical plausibility on multiple benchmarks (CLEVERER, PhysInOne, PhysGaia). We believe that this work opens a scalable pathway toward general-purpose dynamic world models that internalize the 3D invariants of the physical world solely through passive observation of monocular videos.

Reconstructing dynamic 3D scenes from multi-view videos is a foundational task for robotics, AR/VR, and digital twins. While 3D Gaussian Splatting (3DGS) provides state-of-the art scene representation, its dynamic adaptations (4DGS) face significant challenges. Early MLP-based deformation models excel at interpolating within training frames but fail at temporal extrapolation --- important feature for forecasting in predictive systems. To address this, physically grounded approaches have been proposed to enable robust future forecasting, while, concurrently, semantic 4DGS methods have been developed for scene analysis and language-driven prompting. However, there is currently no framework that unites both physical consistency and semantic understanding. In this paper, we propose the first, to the best of our knowledge, unified 4DGS approach that is both physically grounded and semantically aware. Furthermore, to optimize computational efficiency, we introduce a novel rigid-body constraint mechanism. Instead of predicting the physical dynamics for every Gaussian particle, our model predicts the motion of a single anchor Gaussian per semantic object, updating the remaining Gaussians via relative transformations. This architectural design significantly accelerates novel view synthesis compared to an unconstrained baseline, while enabling object-accurate extrapolation and intuitive semantic interaction. Our project page: https://be2rlab.github.io/r5dgs/.