mlsanityData to 14 Oct 2026

WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry

arXiv 2502.06485 ↗First posted 10 Feb 2025cond-mat.mtrl-sci cs.AI cs.LGcited by 26

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

Abstract (arXiv)

Crystalline materials often exhibit a high level of symmetry. However, most generative models do not account for symmetry, but rather model each atom without any constraints on its position or element. We propose a generative model, Wyckoff Diffusion (WyckoffDiff), which generates symmetry-based descriptions of crystals. This is enabled by considering a crystal structure representation that encodes all symmetry, and we design a novel neural network architecture which enables using this representation inside a discrete generative model framework. In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation. We additionally present a new metric, Fr'echet Wrenformer Distance, which captures the symmetry aspects of the materials generated, and we benchmark WyckoffDiff against recently proposed generative models for crystal generation. As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 18 of its 47 references that are in the map. First posted on arXiv 10 Feb 2025.

Builds on

18 of 47 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024Dirichlet Flow Matching with Applications to DNA Sequence Design8 Feb
  2. 2023Crystal Structure Prediction by Joint Equivariant Diffusion30 Jul
  3. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep

Other references · 15

  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. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  7. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  8. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 745
  9. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  10. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
  11. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 270
  12. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 194
3 more
  1. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 169
  2. 2024Space Group Constrained Crystal Generationcited by 73
  3. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 7; 2026: 19.

26 papers.

Sort:

By area:

  1. 2025Space Group Equivariant Crystal Diffusioncited by 15
  2. 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
  3. 2026Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modelingcited by 7
  4. 2025PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesiscited by 5
  5. 2026DMFlow: Disordered Materials Generation by Flow Matchingcited by 5
  6. 2025Generative Models for Crystalline Materialscited by 4
  7. 2025PolyGraph Discrepancy: a classifier-based metric for graph generationcited by 3
  8. 2026CrystalReasoner: Reasoning and RL for Property-Conditioned Crystal Structure Generationcited by 3
  9. 2025Transport Novelty Distance: A Distributional Metric for Evaluating Material Generative Modelscited by 2
  10. 2026SLayerGen: a Crystal Generative Model for all Space and Layer Groupscited by 2
  11. 2026CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Modelscited by 2
  12. 2026How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Sciencecited by 1
14 more
  1. 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modelingcited by 1
  2. 2026Toward Controllable Catalyst Inverse Design via Large-Scale Autoregressive Pretrainingcited by 1
  3. 2026Discovering Crystal Structure Prediction Algorithms with an AI Co-Scientistcited by 1
  4. 2026CrystalGRPO: Target-Aligned and Coverage-Preserving Reinforcement Learning for Flow-Based Crystal Structure Predictioncited by 1
  5. 20253D Shape Generation: A Surveycited by 0
  6. 2026OrgFlow: Generative Modeling of Organic Crystal Structures from Molecular Graphscited by 0
  7. 2026Generating Symmetric Materials using Latent Flow Matchingcited by 0
  8. 2026LapidaryEngine: Fully Conversational Crystal Generationcited by 0
  9. 2026Context-weighted Discrete Flow Matchingcited by 0
  10. 2026Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluationcited by 0
  11. 2026DynaCrys: Crystal Generation with Dynamic Space-Group Diffusioncited by 0
  12. 2026uFlowCSP: Crystal Structure Prediction using Mean flow generative modelscited by 0
  13. 2026Topology-Stratified Materials Discovery with A Flow-Based Generative Modelcited by 0
  14. 2026GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generationcited by 0

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. 2024Discovery of 2D Materials via Symmetry-Constrained Diffusion Model
  3. 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers
  4. 2025LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation
  5. 2025Rethinking Crystal Symmetry Prediction: A Decoupled Perspective
  6. 2026Crystalite: A Lightweight Transformer for Efficient Crystal Modeling
  7. 2025Kinetic Langevin Diffusion for Crystalline Materials Generation
  8. 2023Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells