mlsanityData to 7 Oct 2026

Towards Symmetry-Aware Generation of Periodic Materials

arXiv 2307.02707 ↗First posted 6 Jul 2023cs.LG cond-mat.mtrl-scicited by 25

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Abstract (arXiv)

We consider the problem of generating periodic materials with deep models. While symmetry-aware molecule generation has been studied extensively, periodic materials possess different symmetries, which have not been completely captured by existing methods. In this work, we propose SyMat, a novel material generation approach that can capture physical symmetries of periodic material structures. SyMat generates atom types and lattices of materials through generating atom type sets, lattice lengths and lattice angles with a variational auto-encoder model. In addition, SyMat employs a score-based diffusion model to generate atom coordinates of materials, in which a novel symmetry-aware probabilistic model is used in the coordinate diffusion process. We show that SyMat is theoretically invariant to all symmetry transformations on materials and demonstrate that SyMat achieves promising performance on random generation and property optimization tasks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 34 of its 64 references that are in the map. First posted on arXiv 6 Jul 2023.

Builds on

34 of 64 references.

References · 34

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  8. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  9. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  10. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  11. 2018Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generationcited by 363
  12. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
22 more
  1. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  2. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  3. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  4. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  5. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  6. 2021E(n) Equivariant Normalizing Flowscited by 165
  7. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  8. 2022Generating 3D Molecules for Target Protein Bindingcited by 104
  9. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 104
  10. 2019Molecular geometry prediction using a deep generative graph neural networkcited by 91
  11. 2021Learning Neural Generative Dynamics for Molecular Conformation Generationcited by 87
  12. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  13. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  14. 2021DIG: A Turnkey Library for Diving into Graph Deep Learning Researchcited by 76
  15. 2019A Generative Model for Molecular Distance Geometrycited by 73
  16. 2021An End-to-End Framework for Molecular Conformation Generation via Bilevel Programmingcited by 59
  17. 2020An invertible crystallographic representation for general inverse design of inorganic crystals with targeted propertiescited by 53
  18. 2019Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materialscited by 46
  19. 2023Efficient Approximations of Complete Interatomic Potentials for Crystal Property Predictioncited by 37
  20. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  21. 2021Molecule3D: A Benchmark for Predicting 3D Geometries from Molecular Graphscited by 31
  22. 2022Deep Generative Model for Periodic Graphscited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 11; 2026: 5.

25 papers.

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  1. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  2. 2024Space Group Informed Transformer for Crystalline Materials Generationcited by 40
  3. 2024LLaMP: Large Language Model Made Powerful for High-fidelity Materials Knowledge Retrieval and Distillationcited by 32
  4. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  5. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 20
  6. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  7. 2024MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworkscited by 15
  8. 2025A Periodic Bayesian Flow for Material Generationcited by 15
  9. 2025Periodic Materials Generation using Text-Guided Joint Diffusion Modelcited by 15
  10. 2024Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Datacited by 12
  11. 2025Invariant Tokenization of Crystalline Materials for Language Model Enabled Generationcited by 12
  12. 2025LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generationcited by 12
13 more
  1. 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Surveycited by 9
  2. 2025Equivariant Diffusion for Crystal Structure Predictioncited by 8
  3. 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformerscited by 7
  4. 2024A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Predictioncited by 7
  5. 2025Flow Matching for Collaborative Filteringcited by 7
  6. 2024Efficient Symmetry-Aware Materials Generation via Hierarchical Generative Flow Networkscited by 3
  7. 2025MetamatBench: Integrating Heterogeneous Data, Computational Tools, and Visual Interface for Metamaterial Discoverycited by 2
  8. 2026CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Modelscited by 2
  9. 2025UniMate: A Unified Model for Mechanical Metamaterial Generation, Property Prediction, and Condition Confirmationcited by 1
  10. 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modelingcited by 1
  11. 2026Latent Diffusion Pretraining for Crystal Property Predictioncited by 1
  12. 2026Model Agnostic Graph Prompt Learning for Crystal Property Predictioncited by 0
  13. 2026Text-guided flow matching enables sample-efficient crystal structure generationcited by 0

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  1. 2026Generating Symmetric Materials using Latent Flow Matching
  2. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry
  3. 2023MatterGen: a generative model for inorganic materials design
  4. 2024Discovery of 2D Materials via Symmetry-Constrained Diffusion Model
  5. 2026OxiGen: Oxidation-State-Aware Crystal Generation
  6. 2024FlowMM: Generating Materials with Riemannian Flow Matching
  7. 2025Open Materials Generation with Stochastic Interpolants
  8. 2025CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks