mlsanityData to 7 Oct 2026

Crystal Diffusion Variational Autoencoder for Periodic Material Generation

arXiv 2110.06197 ↗First posted 12 Oct 2021cs.LG cond-mat.mtrl-sci physics.comp-phcited by 268

Not on the map. Why?

Cited by 56 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

Key facts. Cited by 268 papers in the map (data through 7 Oct 2026). Builds on 30 of its 72 references that are in the map. First posted on arXiv 12 Oct 2021.

Builds on

30 of 72 references.

References · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2013Auto-Encoding Variational Bayescited by 3,980
  6. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  9. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 2020Directional Message Passing for Molecular Graphscited by 556
  12. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 487
18 more
  1. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  2. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
  3. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  4. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  5. 2020Learning Gradient Fields for Shape Generationcited by 245
  6. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  7. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  8. 2021On Fast Sampling of Diffusion Probabilistic Modelscited by 170
  9. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  10. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  11. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  12. 2021Learning Neural Generative Dynamics for Molecular Conformation Generationcited by 87
  13. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  14. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  15. 2019Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materialscited by 46
  16. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  17. 2021Crystal structure prediction of materials with high symmetry using differential evolutioncited by 9
  18. 2019Study of Deep Generative Models for Inorganic Chemical Compositionscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 17; 2023: 42; 2024: 50; 2025: 85; 2026: 74.

268 papers.

Sort:

By area:

  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2023Training Diffusion Models with Reinforcement Learningcited by 939
  3. 2022A Survey on Generative Diffusion Modelcited by 238
  4. 2022Graph neural networks for materials science and chemistrycited by 181
  5. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  6. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  7. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  8. 2023MatterGen: a generative model for inorganic materials designcited by 98
  9. 2024Fine-Tuned Language Models Generate Stable Inorganic Materials as Textcited by 92
  10. 2024Physics-Informed Diffusion Modelscited by 88
  11. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  12. 2023A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?cited by 84
38 more
  1. 2022SELFIES and the future of molecular string representationscited by 76
  2. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  3. 2023Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamicscited by 72
  4. 2024Space Group Constrained Crystal Generationcited by 71
  5. 2024Jailbreaking Prompt Attack: A Controllable Adversarial Attack against Diffusion Modelscited by 68
  6. 2023On the Generalization Properties of Diffusion Modelscited by 67
  7. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  8. 2023Scalable Diffusion for Materials Generationcited by 52
  9. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 52
  10. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  11. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  12. 2024LLMatDesign: Autonomous Materials Discovery with Large Language Modelscited by 41
  13. 2024Are LLMs Ready for Real-World Materials Discovery?cited by 40
  14. 2024Space Group Informed Transformer for Crystalline Materials Generationcited by 40
  15. 2022Few-Shot Diffusion Modelscited by 37
  16. 2022Crystal Twins: Self-supervised Learning for Crystalline Material Property Predictioncited by 34
  17. 2023A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Materialcited by 34
  18. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  19. 2022Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraintscited by 30
  20. 2022Exploring Generative Neural Temporal Point Processcited by 30
  21. 2023DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Modelscited by 30
  22. 2025Hypothesis Generation for Materials Discovery and Design Using Goal-Driven and Constraint-Guided LLM Agentscited by 30
  23. 2023Crystal-GFN: sampling crystals with desirable properties and constraintscited by 29
  24. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  25. 2025Open Materials Generation with Stochastic Interpolantscited by 26
  26. 2023Towards Symmetry-Aware Generation of Periodic Materialscited by 25
  27. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetrycited by 25
  28. 2022Equivariant Networks for Crystal Structurescited by 24
  29. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 24
  30. 2025A practical guide to machine learning interatomic potentials -- Status and futurecited by 24
  31. 2023MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Designcited by 23
  32. 2024MMSci: A Dataset for Graduate-Level Multi-Discipline Multimodal Scientific Understandingcited by 23
  33. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  34. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 22
  35. 2022Deep Generative Model for Periodic Graphscited by 20
  36. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 20
  37. 2025Guiding Generative Models to Uncover Diverse and Novel Crystals via Reinforcement Learningcited by 19
  38. 2022Data-driven discovery of novel 2D materials by deep generative modelscited by 18

50 most cited of 268 All 268 (JSON)