# Principia: Relational Physics Tests for Video Models

arXiv: https://arxiv.org/abs/2609.04200 · HTML: https://mlsanity.com/paper/2609.04200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 47 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 30 of 37)

- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Transformers are Sample-Efficient World Models](https://mlsanity.com/paper/2209.00588/) (2022)
- [Video models are zero-shot learners and reasoners](https://mlsanity.com/paper/2509.20328/) (2025)
- [Probing the 3D Awareness of Visual Foundation Models](https://mlsanity.com/paper/2404.08636/) (2024)
- [PhysGen: Rigid-Body Physics-Grounded Image-to-Video Generation](https://mlsanity.com/paper/2409.18964/) (2024)
- [Towards World Simulator: Crafting Physical Commonsense-Based Benchmark for Video Generation](https://mlsanity.com/paper/2410.05363/) (2024)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [PhysBench: Benchmarking and Enhancing Vision-Language Models for Physical World Understanding](https://mlsanity.com/paper/2501.16411/) (2025)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [VideoPhy-2: A Challenging Action-Centric Physical Commonsense Evaluation in Video Generation](https://mlsanity.com/paper/2503.06800/) (2025)
- [PHYRE: A New Benchmark for Physical Reasoning](https://mlsanity.com/paper/1908.05656/) (2019)
- [VideoREPA: Learning Physics for Video Generation through Relational Alignment with Foundation Models](https://mlsanity.com/paper/2505.23656/) (2025)
- [PhysGen3D: Crafting a Miniature Interactive World from a Single Image](https://mlsanity.com/paper/2503.20746/) (2025)
- [Shadows Don't Lie and Lines Can't Bend! Generative Models don't know Projective Geometry...for now](https://mlsanity.com/paper/2311.17138/) (2023)
- [Physion++: Evaluating Physical Scene Understanding that Requires Online Inference of Different Physical Properties](https://mlsanity.com/paper/2306.15668/) (2023)
- [IntPhys 2: Benchmarking Intuitive Physics Understanding In Complex Synthetic Environments](https://mlsanity.com/paper/2506.09849/) (2025)
- [Generative Models: What Do They Know? Do They Know Things? Let's Find Out!](https://mlsanity.com/paper/2311.17137/) (2023)
- [PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop](https://mlsanity.com/paper/2503.09595/) (2025)
- [StyleGAN knows Normal, Depth, Albedo, and More](https://mlsanity.com/paper/2306.00987/) (2023)
- [PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation](https://mlsanity.com/paper/2509.20358/) (2025)
- [NewtonGen: Physics-Consistent and Controllable Text-to-Video Generation via Neural Newtonian Dynamics](https://mlsanity.com/paper/2509.21309/) (2025)
- [T2VPhysBench: A First-Principles Benchmark for Physical Consistency in Text-to-Video Generation](https://mlsanity.com/paper/2505.00337/) (2025)
- [LumiNet: Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting](https://mlsanity.com/paper/2412.00177/) (2024)
- [CausalVQA: A Physically Grounded Causal Reasoning Benchmark for Video Models](https://mlsanity.com/paper/2506.09943/) (2025)
- [A General Protocol to Probe Large Vision Models for 3D Physical Understanding](https://mlsanity.com/paper/2310.06836/) (2023)
- [What about gravity in video generation? Post-Training Newton's Laws with Verifiable Rewards](https://mlsanity.com/paper/2512.00425/) (2025)

## Built on by (most cited first, 2 of 2)

- [How Does Geometry Enter Generated Motion?](https://mlsanity.com/paper/2610.05135/) (2026)
- [World Models' Last Exam in Physics](https://mlsanity.com/paper/2610.08791/) (2026)

## Abstract (arXiv)

Evaluating physical reasoning in video models is difficult because absolute motion measurements depend on frame rate, object scale, and camera calibration, all of which are often ambiguous or unavailable in generated video. We propose a different approach. When two objects in the same scene obey the same physical law, their motions must satisfy predictable relationships, and these relationships hold independent of calibration. We introduce Principia, a benchmark that evaluates Newtonian physics through relational consistency between paired objects. Principia spans eight phenomena - gravity, restitution, friction, rotational inertia, projectile motion, momentum, pendulum, and mass-spring oscillation - across translational, rotational, collisional, and oscillatory dynamics, using real-world scenes recorded under controlled protocols. We also introduce a calibration-independent consistency score that quantifies physical violation directly in image space. Across thousands of generations from six state-of-the-art video generators, no model exceeds 0.42 on Principia despite all scoring around 0.8 on VBench. Vision-language models are evaluated on their ability to detect relational physics violations, with the best model achieving only 67% accuracy and most performing near chance level.