# Symmetry-Aware Bayesian Flow Networks for Crystal Generation

arXiv: https://arxiv.org/abs/2502.03146 · HTML: https://mlsanity.com/paper/2502.03146/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Bayesian Flow Networks](https://mlsanity.com/paper/2308.07037/) (2023)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Normalizing flows for atomic solids](https://mlsanity.com/paper/2111.08696/) (2021)
- [Large-scale machine-learning-assisted exploration of the whole materials space](https://mlsanity.com/paper/2210.00579/) (2022)

## Built on by (most cited first, 9 of 9)

- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [Open Materials Generation with Inference-Time Reinforcement Learning](https://mlsanity.com/paper/2602.00424/) (2026)
- [DMFlow: Disordered Materials Generation by Flow Matching](https://mlsanity.com/paper/2602.04734/) (2026)
- [MiAD: Mirage Atom Diffusion for De Novo Crystal Generation](https://mlsanity.com/paper/2511.14426/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [Unsupervised anomaly detection using Bayesian flow networks: application to brain FDG PET in the context of Alzheimer's disease](https://mlsanity.com/paper/2507.17486/) (2025)
- [DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion](https://mlsanity.com/paper/2608.07401/) (2026)
- [EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations](https://mlsanity.com/paper/2610.01315/) (2026)

## Abstract (arXiv)

The discovery of new crystalline materials is essential to scientific and technological progress. However, traditional trial-and-error approaches are inefficient due to the vast search space. Recent advancements in machine learning have enabled generative models to predict new stable materials by incorporating structural symmetries and to condition the generation on desired properties. In this work, we introduce SymmBFN, a novel symmetry-aware Bayesian Flow Network (BFN) for crystalline material generation that accurately reproduces the distribution of space groups found in experimentally observed crystals. SymmBFN substantially improves efficiency, generating stable structures at least 50 times faster than the next-best method. Furthermore, we demonstrate its capability for property-conditioned generation, enabling the design of materials with tailored properties. Our findings establish BFNs as an effective tool for accelerating the discovery of crystalline materials.