Δynamics: Language-Based Representation for Inferring Rigid-Body Dynamics From Videos

Inferring object dynamics from visual observations is essential for intelligent agents to reason about and interact with the physical world, yet remains challenging due to the fundamental gap between visual evidence and intrinsic dynamics. Existing methods either rely on costly per-scene optimization, limiting efficiency and scalability, or directly map visual evidence to intrinsic dynamics without intermediate physical abstractions, making them prone to appearance and geometry shortcuts. To bridge this gap, we propose Analytic Dynamics, a feed-forward dynamics inference framework that introduces an intermediate physics-grounded dynamics representation between visual observations and intrinsic dynamics. Specifically, we leverage privileged physical states, including position, displacement, and deformation gradient fields, which are available in simulation, to learn a structured dynamics representation that is difficult to discover from visual observations alone. By aligning visual representations with this space, we equip visual models with a physics-grounded inductive bias, guiding them to capture dynamics-relevant patterns for material model classification and parameter regression. To facilitate this research, we develop a dynamics data generation pipeline and benchmark containing paired physical state trajectories, rendered videos, and ground-truth material models and parameters. Extensive experiments demonstrate that Analytic Dynamics achieves efficient, accurate, and generalizable dynamics inference from monocular videos.

Reliable physical reasoning from video requires understanding how objects move, interact, and respond to interventions. Existing vision-language models (VLMs) often struggle to interpret these dynamics and reason reliably about future and counterfactual outcomes. We introduce PhysMind, a training-free agentic framework that constructs one reusable, question-agnostic executable world per video. PhysMind recovers a temporally consistent dynamic scene through object segmentation, mesh reconstruction, and 6D pose tracking, then fits analytic continuous-time dynamics and latent physical parameters without unrolling a time-stepped simulator. Given a question, it inspects, continues, or edits the world and answers from the resulting trajectories and interactions. Relative to direct chain-of-thought (CoT) reasoning with the same VLM, PhysMind improves accuracy by 38.23 points on CLEVRER and 8.08 points on Physion++. On counterfactual questions, it exceeds the strongest evaluated VLM baseline, GPT-5.5, by 19.25 points.

Existing image-to-video generation methods often produce physically implausible motions and lack precise control over object dynamics. While prior approaches have incorporated physics simulators, they remain confined to 2D planar motions and fail to capture depth-aware spatial interactions. We introduce PhysLayer, a novel framework enabling language-guided, depth-aware layered animation of static images. PhysLayer consists of three key components: First, a language-guided scene understanding module that utilizes vision foundation models to decompose scenes into depth-based layers by analyzing object composition, material properties, and physical parameters. Second, a depth-aware layered physics simulation that extends 2D rigid-body dynamics with depth motion and perspective-consistent scaling, enabling more realistic object interactions without requiring full 3D reconstruction. Third, a physics-guided video synthesis module that integrates simulated trajectories with scene-aware relighting for temporally coherent results. Experimental results demonstrate improvements in CLIP-Similarity (+2.2%), FID score (+9.3%), and Motion-FID (+3%), with human evaluation showing enhanced physical plausibility (+24%) and text-video alignment (+35%). Our approach provides a practical balance between physical realism and computational efficiency for controllable image animation.