# How Does Geometry Enter Generated Motion?

arXiv: https://arxiv.org/abs/2610.05135 · HTML: https://mlsanity.com/paper/2610.05135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [LTX-2: Efficient Joint Audio-Visual Foundation Model](https://mlsanity.com/paper/2601.03233/) (2026)
- [VideoPhy: Evaluating Physical Commonsense for Video Generation](https://mlsanity.com/paper/2406.03520/) (2024)
- [Towards World Simulator: Crafting Physical Commonsense-Based Benchmark for Video Generation](https://mlsanity.com/paper/2410.05363/) (2024)
- [Cosmos 3: Omnimodal World Models for Physical AI](https://mlsanity.com/paper/2606.02800/) (2026)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [Seedance 2.0: Advancing Video Generation for World Complexity](https://mlsanity.com/paper/2604.14148/) (2026)
- [Evaluating Newtonian Mechanics in Video Generative Models with Real Physical Systems](https://mlsanity.com/paper/2504.02918/) (2025)
- [Physics-IQ Verified](https://mlsanity.com/paper/2606.18943/) (2026)
- [The Pulse of Motion: Measuring Physical Frame Rate from Visual Dynamics](https://mlsanity.com/paper/2603.14375/) (2026)
- [Objects in Generated Videos Are Slower Than They Appear: Models Suffer Sub-Earth Gravity and Don't Know Galileo's Principle...for now](https://mlsanity.com/paper/2512.02016/) (2025)
- [Twin Rollouts: Noise-Coupled Counterfactual Branching in Interactive Video World Models](https://mlsanity.com/paper/2608.08982/) (2026)
- [RigidBench: Evaluating Rigid-Body Physics in Video Generation Models](https://mlsanity.com/paper/2608.15555/) (2026)
- [Physics in 2-Steps: Locking Motion Priors Before Visual Refinement Erases Them](https://mlsanity.com/paper/2606.06361/) (2026)
- [CaliBench: Are the Stochastic Dynamics of Video World Models Physically Calibrated?](https://mlsanity.com/paper/2608.16829/) (2026)
- [Benchmarking Single-Factor Physical Video-to-Audio Generation](https://mlsanity.com/paper/2605.30339/) (2026)
- [The Seriality Gap in Video Diffusion Models](https://mlsanity.com/paper/2607.13031/) (2026)
- [Principia: Relational Physics Tests for Video Models](https://mlsanity.com/paper/2609.04200/) (2026)
- [PhysWeep: Does a Video Generator Realize the Physics You Ask For?](https://mlsanity.com/paper/2609.06207/) (2026)
- [Why Do Video Diffusion Models Violate Physics? Unveiling the Flaws in Attention Mechanisms](https://mlsanity.com/paper/2609.23658/) (2026)
- [MotionSpec: Spectral Trajectory Supervision for Motion-Consistent Video Generation](https://mlsanity.com/paper/2609.28095/) (2026)
- [MultiEcho: An Experimental Science of Learned Worlds](https://mlsanity.com/paper/2609.33347/) (2026)
- [Foresight at the Event Boundary: Evaluating Physical Prediction in Video World Models](https://mlsanity.com/paper/2609.36531/) (2026)

## Abstract (arXiv)

Under a fixed physical law, the visible geometry of a scene determines how motion must change. We ask how video generators realize this relationship. We fix the law and the initial state and change only the geometry drawn in the first frame, within matched families of tracks and deflectors, and compare each generated trajectory with the simulator prediction for that geometry. Paired interventions change one thing at a time: a local bump, the height of a barrier, the words of the prompt, the length of the clip. Across nine image-to-video models, geometry is preserved and shapes the motion: the speed of the ball follows the drawn undulation of a track. A physical state would carry this response forward, and here the generated motion parts from the law. The mean slope barely accelerates the ball, successive contacts fail to compose through a consistent state, an edit ahead of the ball alters its motion before it arrives, and the ball climbs over barriers higher than its release point. Two global conditions organize the global trajectory: text strongly controls the destination, while clip length strongly controls timing in the open-weight models tested. The pattern persists with photographed first frames. Current video generation thus behaves as geometry-conditioned motion synthesis whose evolution of state differs systematically from that of a fixed physical law.