mlsanityData to 14 Oct 2026

Equivariant Flow Matching with Hybrid Probability Transport

arXiv 2312.07168 ↗First posted 12 Dec 2023cs.LG cs.AIcited by 60

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

Abstract (arXiv)

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in generating feature-rich geometries. However, existing DMs typically suffer from unstable probability dynamics with inefficient sampling speed. In this paper, we introduce geometric flow matching, which enjoys the advantages of both equivariant modeling and stabilized probability dynamics. More specifically, we propose a hybrid probability path where the coordinates probability path is regularized by an equivariant optimal transport, and the information between different modalities is aligned. Experimentally, the proposed method could consistently achieve better performance on multiple molecule generation benchmarks with 4.75× speed up of sampling on average.

Key facts. Cited by 60 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 40 of its 57 references that are in the map. First posted on arXiv 12 Dec 2023.

Builds on

40 of 57 references.

Closest ancestors · 9

Same direction, newest first

  1. 2023Equivariant flow matching26 Jun
  2. 2023Geometric Latent Diffusion Models for 3D Molecule Generation2 May
  3. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
  4. 2022Flow Matching for Generative Modeling6 Oct
  5. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  6. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  7. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models26 May
  8. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  9. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2018Neural Ordinary Differential Equationscited by 3,779
  7. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  8. 2019Generating Diverse High-Fidelity Images with VQ-VAE-2cited by 1,387
  9. 2021Variational Diffusion Modelscited by 1,153
  10. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,027
  11. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  12. 2021E(n) Equivariant Graph Neural Networkscited by 965
19 more
  1. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  2. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 652
  3. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  4. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 305
  5. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  6. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
  7. 2018Formal Limitations on the Measurement of Mutual Informationcited by 189
  8. 2018Constrained Graph Variational Autoencoders for Molecule Designcited by 185
  9. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 185
  10. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 183
  11. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 172
  12. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 106
  13. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  14. 2022DiffBP: Generative Diffusion of 3D Molecules for Target Protein Bindingcited by 58
  15. 2019Equivariant Hamiltonian Flowscited by 39
  16. 2021Learning to design drug-like molecules in three-dimensional space using deep generative modelscited by 37
  17. 2020Generating 3D Molecular Structures Conditional on a Receptor Binding Site with Deep Generative Modelscited by 33
  18. 2022Protein Sequence and Structure Co-Design with Equivariant Translationcited by 31
  19. 2019A Purely Algebraic Justification of the Kabsch-Umeyama Algorithmcited by 24

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 26; 2025: 29; 2026: 5.

60 papers.

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  1. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 122
  2. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 72
  3. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generationcited by 54
  4. 2024MolCRAFT: Structure-Based Drug Design in Continuous Parameter Spacecited by 48
  5. 2024Categorical Flow Matching on Statistical Manifoldscited by 47
  6. 2024Transferable Boltzmann Generatorscited by 46
  7. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 43
  8. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 41
  9. 2024Full-Atom Peptide Design based on Multi-modal Flow Matchingcited by 34
  10. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  11. 2024Training Free Guided Flow Matching with Optimal Controlcited by 25
  12. 2025α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Modelscited by 18
38 more
  1. 2024MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworkscited by 17
  2. 2025Not-So-Optimal Transport Flows for 3D Point Cloud Generationcited by 17
  3. 2025A Periodic Bayesian Flow for Material Generationcited by 16
  4. 2025Beyond Optimal Transport: Model-Aligned Coupling for Flow Matchingcited by 15
  5. 2025Multi-domain Distribution Learning for De Novo Drug Designcited by 15
  6. 2024Geometric Representation Condition Improves Equivariant Molecule Generationcited by 13
  7. 2025Applications of Modular Co-Design for De Novo 3D Molecule Generationcited by 13
  8. 2025Equivariant Neural Diffusion for Molecule Generationcited by 13
  9. 2025UniMoMo: Unified Generative Modeling of 3D Molecules for De Novo Binder Designcited by 12
  10. 2025TABASCO: A Fast, Simplified Model for Molecular Generation with Improved Physical Qualitycited by 12
  11. 2024Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transportcited by 11
  12. 2024Exploring Discrete Flow Matching for 3D De Novo Molecule Generationcited by 11
  13. 2025High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Predictioncited by 11
  14. 2025Flexible MOF Generation with Torsion-Aware Flow Matchingcited by 10
  15. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 9
  16. 2024Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extensioncited by 9
  17. 2025Unified Guidance for Geometry-Conditioned Molecular Generationcited by 9
  18. 2024Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Spacecited by 8
  19. 2025Scalable Autoregressive 3D Molecule Generationcited by 8
  20. 2025Space Group Conditional Flow Matchingcited by 7
  21. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 7
  22. 2025Compositional Flows for 3D Molecule and Synthesis Pathway Co-designcited by 6
  23. 2025Piloting Structure-Based Drug Design via Modality-Specific Optimal Schedulecited by 6
  24. 2025Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matchingcited by 6
  25. 2025Prior-Guided Flow Matching for Target-Aware Molecule Design with Learnable Atom Numbercited by 6
  26. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  27. 2025Scalable and Cost-Efficient de Novo Template-Based Molecular Generationcited by 5
  28. 2025Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteriacited by 5
  29. 2025Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matchingcited by 5
  30. 2026Molecular Representations in Implicit Functional Space via Hyper-Networkscited by 5
  31. 2024SubGDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learningcited by 4
  32. 2024Diffusion Twigs with Loop Guidance for Conditional Graph Generationcited by 4
  33. 2025Disentangling Total-Variance and Signal-to-Noise-Ratio Improves Diffusion Modelscited by 4
  34. 2025Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problemscited by 4
  35. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  36. 20263D Molecule Generation from Rigid Motifs via SE(3) Flowscited by 3
  37. 2026Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fieldscited by 3
  38. 2024Bridging Geometric States via Geometric Diffusion Bridgecited by 2

50 most cited of 60 All 60 (JSON)

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  1. 2025Controlled Generation with Equivariant Variational Flow Matching
  2. 2026Flow Matching is Adaptive to Manifold Structures
  3. 2026Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition
  4. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation
  5. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment
  6. 2022Modular Flows: Differential Molecular Generation
  7. 2024A survey of probabilistic generative frameworks for molecular simulations
  8. 2024Unified Generative Modeling of 3D Molecules via Bayesian Flow Networks