# Crystal-GFN: sampling crystals with desirable properties and constraints

arXiv: https://arxiv.org/abs/2310.04925 · HTML: https://mlsanity.com/paper/2310.04925/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 51 references that are in the map.
- First posted on arXiv 7 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage](https://mlsanity.com/paper/2010.09435/) (2020)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networks](https://mlsanity.com/paper/1810.11203/) (2018)
- [Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints](https://mlsanity.com/paper/2203.14352/) (2022)
- [Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning](https://mlsanity.com/paper/2306.05445/) (2023)
- [Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling](https://mlsanity.com/paper/2308.02165/) (2023)
- [Multi-Fidelity Active Learning with GFlowNets](https://mlsanity.com/paper/2306.11715/) (2023)
- [PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Design](https://mlsanity.com/paper/2211.12020/) (2022)

## Built on by (most cited first, 30 of 31)

- [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)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Open Materials Generation with Stochastic Interpolants](https://mlsanity.com/paper/2502.02582/) (2025)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximization](https://mlsanity.com/paper/2410.15474/) (2024)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [RetroGFN: Diverse and Feasible Retrosynthesis using GFlowNets](https://mlsanity.com/paper/2406.18739/) (2024)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [Artificial Intelligence and Generative Models for Materials Discovery -- A Review](https://mlsanity.com/paper/2508.03278/) (2025)
- [Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers](https://mlsanity.com/paper/2406.09263/) (2024)
- [Space Group Conditional Flow Matching](https://mlsanity.com/paper/2509.23822/) (2025)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [Towards DNA-Encoded Library Generation with GFlowNets](https://mlsanity.com/paper/2404.10094/) (2024)
- [OBELiX: A Curated Dataset of Crystal Structures and Experimentally Measured Ionic Conductivities for Lithium Solid-State Electrolytes](https://mlsanity.com/paper/2502.14234/) (2025)
- [CrystalGym: A New Benchmark for Materials Discovery Using Reinforcement Learning](https://mlsanity.com/paper/2509.23156/) (2025)
- [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)
- [Catalyst GFlowNet for electrocatalyst design: A hydrogen evolution reaction case study](https://mlsanity.com/paper/2510.02142/) (2025)
- [Rooted Absorbed Prefix Trajectory Balance with Submodular Replay for GFlowNet Training](https://mlsanity.com/paper/2603.00454/) (2026)
- [Discrete Compositional Generation via General Soft Operators and Robust Reinforcement Learning](https://mlsanity.com/paper/2506.17007/) (2025)
- [Irresponsible AI: big tech's influence on AI research and associated impacts](https://mlsanity.com/paper/2512.03077/) (2025)
- [Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling](https://mlsanity.com/paper/2602.12045/) (2026)
- [Dynamic Backtracking in GFlowNets: Enhancing Decision Steps with Reward-Dependent Adjustment Mechanisms](https://mlsanity.com/paper/2404.05576/) (2024)
- [Reinforcement Learning on the Discrete Composition Channel of a Crystal Generator: Validated Gains and Reward Hacking](https://mlsanity.com/paper/2610.03880/) (2026)

## Abstract (arXiv)

The discovery of novel solid-state materials, such as electrocatalysts, super-ionic conductors, or photovoltaic materials, plays a critical role in addressing various global challenges. It has, for instance, the potential to significantly improve the efficiency of renewable energy production and storage, thereby making substantial contributions to climate crisis mitigation strategies. In this paper, we introduce Crystal-GFN, a generative model of crystal structures possessing desirable properties and constraints. Operating as a multi-environment, continuous-discrete GFlowNet, it sequentially samples structural attributes of crystalline materials, namely space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physicochemical and geometric hard constraints. We demonstrate the capabilities of Crystal-GFN to efficiently discover diverse and valid crystals with various properties: low predicted formation energy (median -3.2 eV/atom), band gap close to a target value and high density. Overall, Crystal-GFN is a crystal generation method that addresses several existing challenges in the literature and opens promising paths for accelerating materials discovery with machine learning.