Principia

Principia is a benchmark for evaluating whether video generation and vision-language models capture and respect physical relationships between objects.

The benchmark covers eight physical phenomena:

• Gravity
• Friction
• Restitution
• Pendulum motion
• Mass-spring systems
• Momentum transfer
• Rotational inertia
• Projectile motion

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Motivation

Current video-generation benchmarks largely evaluate visual quality, semantic alignment, and general video consistency. These metrics do not necessarily determine whether generated videos obey basic physical laws.

For example, a generated video may look visually plausible while exhibiting an incorrect relationship between the height and time of flight of two objects under gravity.

Principia instead evaluates physical consistency through relational invariants.

This formulation reduces dependence on absolute quantities such as:

• camera calibration
• scene scale
• frame rate

and focuses on whether the relationship predicted by the physical law is preserved.

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Dataset Structure

Each physical scenario is organized into individual samples:

Principia/
├── restitution/
│   ├── sample_1/
│   │   ├── frame_0000.png
│   │   └── metadata.json
│   ├── sample_2/
│   │   ├── frame_0000.png
│   │   └── metadata.json
│   └── ...
│
├── friction/
│   └── ...
│
├── pendulum/
│   └── ...
│
├── mass_spring/
│   └── ...
│
├── momentum/
│   └── ...
│
├── rotational_inertia/
│   └── ...
│
└── projectile/
    └── ...

Each sample contains:

• first_frame.png — the initial frame/conditioning image for the physical scene.
• metadata.json — scene information, object information, and the relevant physical relationship.

The first frame can be used as the conditioning input for image-to-video generation models.

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Dataset Limitations

Principia evaluates a selected set of controlled physical phenomena and should not be interpreted as a comprehensive test of physical reasoning.

In particular:

• The benchmark focuses on controlled scenarios rather than unconstrained real-world environments.
• Camera motion and visual ambiguity can affect object tracking and measurement.
• Performance on Principia does not necessarily imply general physical understanding.

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Citation

If you use the Principia dataset or benchmark in your research, please cite:

@misc{thozhiyoor2026principiarelationalphysicstests,
  title={Principia: Relational Physics Tests for Video Models},
  author={Varun Varma Thozhiyoor and Shivam Tripathi and Venkatesh Babu Radhakrishnan and Anand Bhattad},
  year={2026},
  eprint={2609.04200},
  archivePrefix={arXiv},
  primaryClass={cs.CV},
  url={https://arxiv.org/abs/2609.04200}
}

@InProceedings{Thozhiyoor_2026_CVPR,
  author    = {Thozhiyoor, Varun Varma and Tripathi, Shivam and Radhakrishnan, Venkatesh Babu and Bhattad, Anand},
  title     = {Objects in Generated Videos Are Slower Than They Appear: Models Suffer Sub-Earth Gravity and Don't Know Galileo's Principle...for now},
  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Findings},
  month     = {June},
  year      = {2026},
  pages     = {3830-3839}
}