# DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion

arXiv: https://arxiv.org/abs/2608.07401 · HTML: https://mlsanity.com/paper/2608.07401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)
- [WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry](https://mlsanity.com/paper/2502.06485/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [Symmetry-Aware Bayesian Flow Networks for Crystal Generation](https://mlsanity.com/paper/2502.03146/) (2025)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)

## Abstract (arXiv)

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires jointly modeling discrete crystallographic symmetry, elemental composition, and continuous geometry. We introduce DynaCrys, a generative model for crystals in which the space group co-evolves with Wyckoff occupations and elements through a coupled symbolic diffusion process. The structured space-group transitions follow crystallographic group-subgroup relations. As the space group changes, a shared, pretrained symmetry codebook provides both the legality-constrained stochastic decoder and the symmetry-constrained crystal-geometry model with a common representation of the corresponding Wyckoff vocabulary. Across large-scale evaluations using two independent relaxation-and-evaluation engines, DynaCrys achieves best-in-class performance in symmetry-aware discovery of stable, unique, and novel crystals, both overall and under the additional requirement of nontrivial post-relaxation symmetry. It also enables fast sampling while generating structures with consistently low relaxation-induced structural displacements.