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PCFM: Physics-Constrained Flow Matching

arXiv  •  Project Page  •  Julia Version

Utkarsh*Pengfei Cai* • Alan Edelman • Rafael Gómez-Bombarelli • Christopher Rackauckas

NeurIPS 2025

This repo implements Physics-Constrained Flow Matching (PCFM) -- a framework that enforces physical constraints during sampling of flow-based generative models.

PCFM summary figure

License

PCFM is released under the MIT License.

This repository includes components derived from amazon-science/ECI-sampling licensed under the Apache License 2.0. See LICENSE, LICENSE-APACHE-2.0, and NOTICE for details.

Citation

If you use this repository, please cite:

@article{PCFM2025,
  title={Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints},
  author={Utkarsh, Utkarsh and Cai, Pengfei and Edelman, Alan and Gomez-Bombarelli, Rafael and Rackauckas, Christopher Vincent},
  journal={arXiv preprint arXiv:2506.04171},
  year={2025}
}

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Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints (NeurIPS 2025)

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