mlsanityData to 7 Oct 2026

Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities

arXiv 2006.02425 ↗First posted 3 Jun 2020stat.ML cs.LG physics.chem-phcited by 248

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Cited by 72 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry. To scale and generalize these results, it is essential that the natural symmetries in the probability density -- in physics defined by the invariances of the target potential -- are built into the flow. We provide a theoretical sufficient criterion showing that the distribution generated by textitequivariant normalizing flows is invariant with respect to these symmetries by design. Furthermore, we propose building blocks for flows which preserve symmetries which are usually found in physical/chemical many-body particle systems. Using benchmark systems motivated from molecular physics, we demonstrate that those symmetry preserving flows can provide better generalization capabilities and sampling efficiency.

Key facts. Cited by 248 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jun 2020.

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Citing papers per year: 2021: 24; 2022: 36; 2023: 49; 2024: 51; 2025: 51; 2026: 37.

248 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  3. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  4. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  5. 2022Riemannian Score-Based Generative Modellingcited by 216
  6. 2023SE(3) diffusion model with application to protein backbone generationcited by 214
  7. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  8. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 176
  9. 2021E(n) Equivariant Normalizing Flowscited by 165
  10. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  11. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  12. 2023Equivariant flow matchingcited by 131
38 more
  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  3. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 99
  4. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  5. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  6. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 79
  7. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  8. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 74
  9. 2022Equivariant Energy-Guided SDE for Inverse Molecular Designcited by 72
  10. 2023A Comprehensive Survey on Deep Graph Representation Learningcited by 72
  11. 2024EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learningcited by 72
  12. 2022A Survey on Deep Graph Generation: Methods and Applicationscited by 69
  13. 2023Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamicscited by 62
  14. 2023Equivariant Flow Matching with Hybrid Probability Transportcited by 59
  15. 2022MDM: Molecular Diffusion Model for 3D Molecule Generationcited by 58
  16. 2022DiffBP: Generative Diffusion of 3D Molecules for Target Protein Bindingcited by 58
  17. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  18. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  19. 2023Clifford Group Equivariant Neural Networkscited by 54
  20. 2021Smooth Normalizing Flowscited by 52
  21. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  22. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 52
  23. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generationcited by 50
  24. 2023Mosaic-SDF for 3D Generative Modelscited by 48
  25. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  26. 2023Geometric Algebra Transformercited by 46
  27. 2021Particle Cloud Generation with Message Passing Generative Adversarial Networkscited by 45
  28. 2024Improved motif-scaffolding with SE(3) flow matchingcited by 43
  29. 2024Transferable Boltzmann Generatorscited by 43
  30. 2023Learning Interpolations between Boltzmann Densitiescited by 42
  31. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  32. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  33. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
  34. 2021Normalizing flows for atomic solidscited by 39
  35. 2022So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systemscited by 39
  36. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  37. 20233D molecule generation by denoising voxel gridscited by 38
  38. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37

50 most cited of 248 All 248 (JSON)