mlsanityData to 7 Oct 2026

Equivariant Diffusion for Crystal Structure Prediction

arXiv 2512.07289 ↗First posted 8 Dec 2025cond-mat.mtrl-sci cs.LGcited by 8

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

Abstract (arXiv)

In addressing the challenge of Crystal Structure Prediction (CSP), symmetry-aware deep learning models, particularly diffusion models, have been extensively studied, which treat CSP as a conditional generation task. However, ensuring permutation, rotation, and periodic translation equivariance during diffusion process remains incompletely addressed. In this work, we propose EquiCSP, a novel equivariant diffusion-based generative model. We not only address the overlooked issue of lattice permutation equivariance in existing models, but also develop a unique noising algorithm that rigorously maintains periodic translation equivariance throughout both training and inference processes. Our experiments indicate that EquiCSP significantly surpasses existing models in terms of generating accurate structures and demonstrates faster convergence during the training process.

Key facts. Cited by 8 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 27 of its 65 references that are in the map. First posted on arXiv 8 Dec 2025.

Builds on

27 of 65 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023Crystal Structure Prediction by Joint Equivariant Diffusion30 Jul
  2. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  3. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  4. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  5. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 22

  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. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  6. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  7. 2016Variational Graph Auto-Encoderscited by 1,373
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  12. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
10 more
  1. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  2. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  3. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  4. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  5. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  6. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  7. 2020An invertible crystallographic representation for general inverse design of inorganic crystals with targeted propertiescited by 53
  8. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  9. 2023Towards Symmetry-Aware Generation of Periodic Materialscited by 25
  10. 2021Crystal structure prediction of materials with high symmetry using differential evolutioncited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 7.

8 papers.

  1. 2026DMFlow: Disordered Materials Generation by Flow Matchingcited by 5
  2. 2026SLayerGen: a Crystal Generative Model for all Space and Layer Groupscited by 2
  3. 2026CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Modelscited by 2
  4. 2025CrystalFormer-CSP: Thinking Fast and Slow for Crystal Structure Predictioncited by 1
  5. 2026EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusioncited by 1
  6. 2026Quotient-Space Diffusion Modelscited by 0
  7. 2026Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependencecited by 0
  8. 2026EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotationscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation
  2. 2023Vector Field Oriented Diffusion Model for Crystal Material Generation
  3. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry
  4. 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers
  5. 2025Equivariant Neural Diffusion for Molecule Generation
  6. 2025Frame-based Equivariant Diffusion Models for 3D Molecular Generation
  7. 2025Symmetry-Aware Generative Modeling through Learned Canonicalization
  8. 2025CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks