mlsanityData to 7 Oct 2026

FlowMM: Generating Materials with Riemannian Flow Matching

arXiv 2406.04713 ↗First posted 7 Jun 2024cs.LG cond-mat.mtrl-sci cs.AIcited by 105

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Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

Key facts. Cited by 105 papers in the map (data through 7 Oct 2026). Builds on 34 of its 63 references that are in the map. First posted on arXiv 7 Jun 2024.

Builds on

34 of 63 references.

References · 34

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  7. 2021E(n) Equivariant Graph Neural Networkscited by 951
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  9. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  10. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
  11. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  12. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
22 more
  1. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  2. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  3. 2022e3nn: Euclidean Neural Networkscited by 171
  4. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  5. 2020Riemannian Continuous Normalizing Flowscited by 143
  6. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  7. 2022Riemannian Diffusion Modelscited by 120
  8. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  9. 2023MatterGen: a generative model for inorganic materials designcited by 98
  10. 2024Fine-Tuned Language Models Generate Stable Inorganic Materials as Textcited by 92
  11. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  12. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  13. 2023Language models can generate molecules, materials, and protein binding sites directly in three dimensions as XYZ, CIF, and PDB filescited by 59
  14. 2023Scalable Diffusion for Materials Generationcited by 52
  15. 2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
  16. 2023On Kinetic Optimal Probability Paths for Generative Modelscited by 42
  17. 2021Normalizing flows for atomic solidscited by 39
  18. 2020Neural Ordinary Differential Equations on Manifoldscited by 31
  19. 2023Crystal-GFN: sampling crystals with desirable properties and constraintscited by 29
  20. 2022Large-scale machine-learning-assisted exploration of the whole materials spacecited by 13
  21. 2021Crystal structure prediction of materials with high symmetry using differential evolutioncited by 9
  22. 2021Interpretable discovery of new semiconductors with machine learningcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 53; 2026: 45.

105 papers.

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  1. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  2. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 52
  3. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  4. 2025Open Materials Generation with Stochastic Interpolantscited by 26
  5. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 24
  6. 2025FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generationcited by 20
  7. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 20
  8. 2025Guiding Generative Models to Uncover Diverse and Novel Crystals via Reinforcement Learningcited by 19
  9. 2024MatExpert: Decomposing Materials Discovery by Mimicking Human Expertscited by 18
  10. 2024Foundational Large Language Models for Materials Researchcited by 18
  11. 2024MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworkscited by 15
  12. 2025A Periodic Bayesian Flow for Material Generationcited by 15
38 more
  1. 2025Periodic Materials Generation using Text-Guided Joint Diffusion Modelcited by 15
  2. 2025Space Group Equivariant Crystal Diffusioncited by 15
  3. 2025Invariant Tokenization of Crystalline Materials for Language Model Enabled Generationcited by 12
  4. 2025LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generationcited by 12
  5. 2025PLaID++: A Preference Aligned Language Model for Targeted Inorganic Materials Designcited by 11
  6. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  7. 2025Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometrycited by 10
  8. 2025High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Predictioncited by 10
  9. 2025Toward Greater Autonomy in Materials Discovery Agents: Unifying Planning, Physics, and Scientistscited by 10
  10. 2025All that structure matches does not glittercited by 10
  11. 2025Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifoldscited by 10
  12. 2024Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materialscited by 9
  13. 2025Symmetry-Aware Bayesian Flow Networks for Crystal Generationcited by 9
  14. 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Surveycited by 9
  15. 2025Flexible MOF Generation with Torsion-Aware Flow Matchingcited by 9
  16. 2025Kinetic Langevin Diffusion for Crystalline Materials Generationcited by 9
  17. 2026Crystalite: A Lightweight Transformer for Efficient Crystal Modelingcited by 9
  18. 2025Establishing baselines for generative discovery of inorganic crystalscited by 8
  19. 2025Siamese Foundation Models for Crystal Structure Predictioncited by 8
  20. 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
  21. 2025Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generationcited by 7
  22. 2025TopoMAS: Large Language Model Driven Topological Materials Multiagent Systemcited by 6
  23. 2025CrystalDiT: A Diffusion Transformer for Crystal Generationcited by 6
  24. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  25. 2026Open Materials Generation with Inference-Time Reinforcement Learningcited by 6
  26. 2025CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walkscited by 5
  27. 2025deCIFer: Crystal Structure Prediction from Powder Diffraction Data using Autoregressive Language Modelscited by 5
  28. 2025Unified Cross-Scale 3D Generation and Understanding via Autoregressive Modelingcited by 5
  29. 2025Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystalscited by 5
  30. 2025Mofasa: A Step Change in Metal-Organic Framework Generationcited by 5
  31. 2025Boltzmann generators for amorphous particle systemscited by 5
  32. 2026DMFlow: Disordered Materials Generation by Flow Matchingcited by 5
  33. 2026MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matchingcited by 5
  34. 2025Guided Diffusion for the Discovery of New Superconductorscited by 4
  35. 2025SE(3)-PoseFlow: Estimating 6D Pose Distributions for Uncertainty-Aware Robotic Manipulationcited by 4
  36. 2025OXtal: An All-Atom Diffusion Model for Organic Crystal Structure Predictioncited by 4
  37. 2026Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modelingcited by 4
  38. 2025GGBall: Graph Generative Model on Poincar'e Ballcited by 3

50 most cited of 105 All 105 (JSON)

Similar, not cited

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  1. 2025WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry
  2. 2025Space Group Conditional Flow Matching
  3. 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling
  4. 2023Towards Symmetry-Aware Generation of Periodic Materials
  5. 2024Structural Constraint Integration in Generative Model for Discovery of Quantum Material Candidates
  6. 2024Discovery of 2D Materials via Symmetry-Constrained Diffusion Model
  7. 2026OxiGen: Oxidation-State-Aware Crystal Generation
  8. 2024Unleashing the power of novel conditional generative approaches for new materials discovery