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Principia: Relational Physics Tests for Video Models
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Introduces Principia, a calibration-independent relational benchmark of paired-object physics scenes (8 Newtonian phenomena) plus a pixel-space consistency score, showing that six video generators score at most ~0.42 and VLMs detect violations near chance.
Problem
Evaluating physical reasoning in video generators and VLMs is hard because absolute motion measurements depend on frame rate, scale, and camera calibration, which are ambiguous in generated video.
Approach
Test relational invariants between two objects obeying the same physical law (e.g., equal arrival times for different masses on an incline), scored in image space via a normalized ratio-based consistency score that needs no metric calibration.
Key results
- Wan2.2-14B achieves the best overall Principia score of 0.419, and no video generator exceeds 0.42 despite ~0.8 VBench scores.
- Gemini-3-Flash is the best VLM at 0.661 overall agreement, with the top single VLM accuracy of 67% on detecting violations.
- Scaling within families is uneven: Cosmos 2B to 14B regresses on restitution and Wan 5B to 14B regresses on momentum.
Surprising findings
- Larger model size does not uniformly improve physical consistency; Gemini-3.1-Pro scores below Gemini-3-Flash and Qwen-32B below Qwen-4B on overall agreement.
- Compute does not predict fidelity: Cosmos-2.5-14B uses more compute than Wan2.2-14B yet scores 0.22 lower.
Limitations
- Covers only macroscopic Newtonian mechanics; excludes fluids, soft bodies, thermodynamics.
- Hallucinated or deformed objects are not separated from genuine physics violations.
- Projectile scoring is sensitive to horizontal camera pan, a binary ordering with no partial credit.
Experimental setup
Datasets: Principia real-world scenes Principia-Synth (Isaac Sim / Omniverse rendered)
Benchmarks: Principia Principia-Synth VBench
Metrics: relational consistency score S_phi agreement score A_phi directional consistency score
Baselines: VBench Physics-IQ Morpheus VideoPhy PhysBench
Builds on: Galileo's equivalence protocol (Thozhiyoor et al.) VBench SAM3 Isaac Sim
Closest papers by meaning
- Apple-$\pi$: Benchmarking Thinking with Video Towards Law-Grounded Physical Intelligence (NeurIPS 2026 · similarity 0.86)
- PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation (NeurIPS 2025 · similarity 0.85)
- How Far Is Video Generation from World Model: A Physical Law Perspective (ICML 2025 · similarity 0.84)
- VideoREPA: Learning Physics for Video Generation through Relational Alignment with Foundation Models (NeurIPS 2025 · similarity 0.84)
- VideoPhy: Evaluating Physical Commonsense for Video Generation (ICLR 2025 · similarity 0.84)
- Physics-Informed Video Generation via Mixture-of-Experts Latent Alignment (NeurIPS 2026 · similarity 0.84)
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