mlsanityData to 14 Oct 2026

Space Group Equivariant Crystal Diffusion

arXiv 2505.10994 ↗First posted 16 May 2025cond-mat.mtrl-sci cs.AIcited by 15

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Abstract (arXiv)

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiD-iff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 43 of its 110 references that are in the map. First posted on arXiv 16 May 2025.

Builds on

43 of 110 references.

References · 43

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Flow Matching for Generative Modelingcited by 5,702
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  7. 2013Auto-Encoding Variational Bayescited by 4,053
  8. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  9. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  11. 2021E(n) Equivariant Graph Neural Networkscited by 965
  12. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
31 more
  1. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 392
  2. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  3. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 270
  4. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
  5. 2017Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learningcited by 192
  6. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 168
  7. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 148
  8. 2018Universal approximations of invariant maps by neural networkscited by 127
  9. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 109
  10. 2024Fine-Tuned Language Models Generate Stable Inorganic Materials as Textcited by 93
  11. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 84
  12. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
  13. 2024Space Group Constrained Crystal Generationcited by 73
  14. 2023Bayesian Flow Networkscited by 63
  15. 2023Scalable Diffusion for Materials Generationcited by 54
  16. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 53
  17. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51
  18. 2019Equivariant Hamiltonian Flowscited by 39
  19. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  20. 2025Open Materials Generation with Stochastic Interpolantscited by 28
  21. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 27
  22. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetrycited by 26
  23. 2021Equivariant Manifold Flowscited by 20
  24. 2025A Periodic Bayesian Flow for Material Generationcited by 16
  25. 2024Generative Hierarchical Materials Searchcited by 13
  26. 2025Invariant Tokenization of Crystalline Materials for Language Model Enabled Generationcited by 12
  27. 2025Symmetry-Aware Bayesian Flow Networks for Crystal Generationcited by 9
  28. 2024A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Predictioncited by 8
  29. 2024GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networkscited by 5
  30. 2024Designing Mechanical Meta-Materials by Learning Equivariant Flowscited by 4
  31. 2025Understanding and Mitigating Distribution Shifts For Machine Learning Force Fieldscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 12.

15 papers.

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  1. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 23
  2. 2025Space Group Conditional Flow Matchingcited by 7
  3. 2026Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modelingcited by 7
  4. 2026Crys-JEPA: Accelerating Crystal Discovery via Embedding Screening and Generative Refinementcited by 4
  5. 2026SLayerGen: a Crystal Generative Model for all Space and Layer Groupscited by 2
  6. 2026CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Modelscited by 2
  7. 2025A Single Architecture for Representing Invariance Under Any Space Groupcited by 1
  8. 2026How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Sciencecited by 1
  9. 2026Composable Crystals: Controllable Materials Discovery via Concept Learningcited by 1
  10. 2026OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discoverycited by 1
  11. 2026OrgFlow: Generative Modeling of Organic Crystal Structures from Molecular Graphscited by 0
  12. 2026Generating Symmetric Materials using Latent Flow Matchingcited by 0
3 more
  1. 2026PRISMat: Policy-Driven, Permutation-Invariant Autoregressive Material Generationcited by 0
  2. 2026DynaCrys: Crystal Generation with Dynamic Space-Group Diffusioncited by 0
  3. 2026Symmetry-Breaking De Novo Crystal Generation via Markovian Jump Diffusioncited by 0