mlsanityData to 7 Oct 2026

Crystal Structure Prediction by Joint Equivariant Diffusion

arXiv 2309.04475 ↗First posted 30 Jul 2023cond-mat.mtrl-sci cs.LGcited by 142

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Crystal Structure Prediction (CSP) is crucial in various scientific disciplines. While CSP can be addressed by employing currently-prevailing generative models (e.g. diffusion models), this task encounters unique challenges owing to the symmetric geometry of crystal structures -- the invariance of translation, rotation, and periodicity. To incorporate the above symmetries, this paper proposes DiffCSP, a novel diffusion model to learn the structure distribution from stable crystals. To be specific, DiffCSP jointly generates the lattice and atom coordinates for each crystal by employing a periodic-E(3)-equivariant denoising model, to better model the crystal geometry. Notably, different from related equivariant generative approaches, DiffCSP leverages fractional coordinates other than Cartesian coordinates to represent crystals, remarkably promoting the diffusion and the generation process of atom positions. Extensive experiments verify that our DiffCSP significantly outperforms existing CSP methods, with a much lower computation cost in contrast to DFT-based methods. Moreover, the superiority of DiffCSP is also observed when it is extended for ab initio crystal generation.

Key facts. Cited by 142 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 39 of its 75 references that are in the map. First posted on arXiv 30 Jul 2023.

Builds on

39 of 75 references.

Closest ancestors · 4

Same direction, newest first

  1. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  2. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  3. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  4. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar

Other references · 35

  1. 2017Attention Is All You Needcited by 59,932
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  9. 2016Variational Graph Auto-Encoderscited by 1,373
  10. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  11. 2021E(n) Equivariant Graph Neural Networkscited by 951
  12. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
23 more
  1. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  2. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  3. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  4. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  5. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  6. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  7. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  8. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  9. 2022Riemannian Score-Based Generative Modellingcited by 216
  10. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  11. 2022EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equationscited by 172
  12. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  13. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  14. 2022Riemannian Diffusion Modelscited by 120
  15. 2022The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalystscited by 95
  16. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  17. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  18. 2022Equivariant Energy-Guided SDE for Inverse Molecular Designcited by 72
  19. 2020An invertible crystallographic representation for general inverse design of inorganic crystals with targeted propertiescited by 53
  20. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  21. 2018CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networkscited by 31
  22. 2021Crystal structure prediction of materials with high symmetry using differential evolutioncited by 9
  23. 2014Efficient Evaluation of the Probability Density Function of a Wrapped Normal Distributioncited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 20; 2025: 63; 2026: 56.

142 papers.

Sort:

By area:

  1. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  2. 2023MatterGen: a generative model for inorganic materials designcited by 98
  3. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  4. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  5. 2024Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspectivecited by 54
  6. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 52
  7. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  8. 2024Are LLMs Ready for Real-World Materials Discovery?cited by 40
  9. 2024Space Group Informed Transformer for Crystalline Materials Generationcited by 40
  10. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  11. 2025Open Materials Generation with Stochastic Interpolantscited by 26
  12. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetrycited by 25
38 more
  1. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 24
  2. 2023MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Designcited by 23
  3. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 20
  4. 2025Guiding Generative Models to Uncover Diverse and Novel Crystals via Reinforcement Learningcited by 19
  5. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  6. 2024MatExpert: Decomposing Materials Discovery by Mimicking Human Expertscited by 18
  7. 2024Foundational Large Language Models for Materials Researchcited by 18
  8. 2024MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworkscited by 15
  9. 2025Periodic Materials Generation using Text-Guided Joint Diffusion Modelcited by 15
  10. 2025Space Group Equivariant Crystal Diffusioncited by 15
  11. 2024Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Datacited by 12
  12. 2025Invariant Tokenization of Crystalline Materials for Language Model Enabled Generationcited by 12
  13. 2025LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generationcited by 12
  14. 2025PLaID++: A Preference Aligned Language Model for Targeted Inorganic Materials Designcited by 11
  15. 2025LLEMA: Evolutionary Search with LLMs for Multi-Objective Materials Discoverycited by 11
  16. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  17. 2025Toward Greater Autonomy in Materials Discovery Agents: Unifying Planning, Physics, and Scientistscited by 10
  18. 2025All that structure matches does not glittercited by 10
  19. 2024Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materialscited by 9
  20. 2025Symmetry-Aware Bayesian Flow Networks for Crystal Generationcited by 9
  21. 2025Riemannian Variational Flow Matching for Material and Protein Designcited by 9
  22. 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Surveycited by 9
  23. 2025Flexible MOF Generation with Torsion-Aware Flow Matchingcited by 9
  24. 2025Kinetic Langevin Diffusion for Crystalline Materials Generationcited by 9
  25. 2026Crystalite: A Lightweight Transformer for Efficient Crystal Modelingcited by 9
  26. 2025Establishing baselines for generative discovery of inorganic crystalscited by 8
  27. 2025Siamese Foundation Models for Crystal Structure Predictioncited by 8
  28. 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
  29. 2025Equivariant Diffusion for Crystal Structure Predictioncited by 8
  30. 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformerscited by 7
  31. 2025MatLLMSearch: Crystal Structure Discovery with Evolution-Guided Large Language Modelscited by 7
  32. 2025A Survey of AI for Materials Science: Foundation Models, LLM Agents, Datasets, and Toolscited by 7
  33. 2025TopoMAS: Large Language Model Driven Topological Materials Multiagent Systemcited by 6
  34. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  35. 2025deCIFer: Crystal Structure Prediction from Powder Diffraction Data using Autoregressive Language Modelscited by 5
  36. 2025Sampling 3D Molecular Conformers with Diffusion Transformerscited by 5
  37. 2025Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystalscited by 5
  38. 2025Boltzmann generators for amorphous particle systemscited by 5

50 most cited of 142 All 142 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2025CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks
  2. 2023Vector Field Oriented Diffusion Model for Crystal Material Generation
  3. 2024Space Group Constrained Crystal Generation
  4. 2023Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling
  5. 2024Discovery of 2D Materials via Symmetry-Constrained Diffusion Model
  6. 2026Finetuning-Free Diffusion Model with Adaptive Constraint Guidance for Inorganic Crystal Structure Generation
  7. 2023Scalable Diffusion for Materials Generation
  8. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation