mlsanityData to 14 Oct 2026

Generating Symmetric Materials using Latent Flow Matching

arXiv 2605.10115 ↗First posted 11 May 2026cs.LG cond-mat.mtrl-scicited by 0

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

Abstract (arXiv)

Tackling the task of materials generation, we aim to enhance the previously proposed All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of materials based on Wyckoff positions. We follow ADiT and perform generative modelling in latent space, adapted to our symmetry-aware representation. By forcing the output of the generative model to adhere to the symmetry restrictions imposed by the generated crystal's space group and each atom's Wyckoff-position, the generated materials exhibit more realistic symmetry properties. We benchmark our method against both symmetry-aware and symmetry-agnostic models for materials generation and show competitive performance, generating stable, symmetric materials with a simple Transformer architecture.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 22 of its 52 references that are in the map. First posted on arXiv 11 May 2026.

Builds on

22 of 52 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025CrystalDiT: A Diffusion Transformer for Crystal Generation13 Aug
  2. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation3 Jul
  3. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materials5 Mar
  4. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry10 Feb
  5. 2023Crystal Structure Prediction by Joint Equivariant Diffusion30 Jul
  6. 2023SE(3) diffusion model with application to protein backbone generation5 Feb
  7. 2022Flow Matching for Generative Modeling6 Oct

Other references · 15

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2022Scalable Diffusion Models with Transformerscited by 6,054
  6. 2022Classifier-Free Diffusion Guidancecited by 5,847
  7. 2015Variational Inference with Normalizing Flowscited by 2,170
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  9. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  10. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 270
  11. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 109
  12. 2024Space Group Constrained Crystal Generationcited by 73
3 more
  1. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51
  2. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 27
  3. 2025Space Group Equivariant Crystal Diffusioncited by 15

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Close in wording, no citation either way

  1. 2023Towards Symmetry-Aware Generation of Periodic Materials
  2. 2024Discovery of 2D Materials via Symmetry-Constrained Diffusion Model
  3. 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling
  4. 2026Crystalite: A Lightweight Transformer for Efficient Crystal Modeling
  5. 2025Kinetic Langevin Diffusion for Crystalline Materials Generation
  6. 2025LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation
  7. 2023MatterGen: a generative model for inorganic materials design
  8. 2026GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation