# Where Should Physics Enter a Molecular Crystal Generator?

arXiv: https://arxiv.org/abs/2609.36398 · HTML: https://mlsanity.com/paper/2609.36398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [DiffusionNFT: Online Diffusion Reinforcement with Forward Process](https://mlsanity.com/paper/2509.16117/) (2025)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation](https://mlsanity.com/paper/2605.13724/) (2026)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [MeanFlowNFT: Bringing Forward-Process RL to Average-Velocity Generators](https://mlsanity.com/paper/2607.15273/) (2026)
- [Generative Design of Crystal Structures by Point Cloud Representations and Diffusion Model](https://mlsanity.com/paper/2401.13192/) (2024)
- [Fast Organic Crystal Structure Prediction with Unit Cell Flow Matching](https://mlsanity.com/paper/2606.03199/) (2026)

## Abstract (arXiv)

Generative models make molecular crystal structure prediction fast, but their samples still exhibit geometric and packing violations. Physics can be introduced during training, post-training, or inference, yet these choices are rarely compared with the generator and physical signal held fixed. We introduce CrystAF, an all-atom crystal flow-map generation model, and use it with the UMA interatomic potential to systematically study where physics should enter. Post-training learns physical preferences directly into CrystAF, improving molecular validity and crystal packing while leaving sampling unchanged: physics is paid for once during training rather than repeatedly at deployment. In contrast, UMA relaxation is effective at repairing local clashes but makes generation 6--26× slower, while learning from relaxed targets provides little benefit. These routes are complementary rather than competing. Physics-informed post-training first shifts the generated distribution toward more physically reasonable structures, after which inexpensive inference-time corrections further remove clashes and restore stereochemistry that the generator cannot represent. Importantly, the same post-training strategy also improves the multi-step all-atom Clari-M and rigid-body MolCrystalFlow generators, demonstrating transfer across architectures and representations. Together, our results suggest a simple principle: learn reusable physical alignment into the generator, and reserve inference-time physics for residual constraints that are better corrected than learned.