mlsanityData to 7 Oct 2026

Equivariant Manifold Flows

arXiv 2107.08596 ↗First posted 19 Jul 2021stat.ML cs.LG math.DGcited by 20

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Abstract (arXiv)

Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications these distributions must respect manifold symmetries -- a trait which most previous models disregard. In this paper, we lay the theoretical foundations for learning symmetry-invariant distributions on arbitrary manifolds via equivariant manifold flows. We demonstrate the utility of our approach by using it to learn gauge invariant densities over SU(n) in the context of quantum field theory.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 25 of its 49 references that are in the map. First posted on arXiv 19 Jul 2021.

Builds on

25 of 49 references.

References · 25

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13 more
  1. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  2. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
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  8. 2020Neural Manifold Ordinary Differential Equationscited by 81
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  10. 2020Latent Variable Modelling with Hyperbolic Normalizing Flowscited by 49
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 8; 2024: 3; 2025: 2; 2026: 3.

20 papers.

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  1. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  2. 2023Equivariant flow matchingcited by 131
  3. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 35
  4. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  5. 2022Symmetry-Based Representations for Artificial and Biological General Intelligencecited by 26
  6. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  7. 2023Riemannian Residual Neural Networkscited by 21
  8. 2023Scaling Riemannian Diffusion Modelscited by 18
  9. 2025Space Group Equivariant Crystal Diffusioncited by 15
  10. 2021Equivariant Finite Normalizing Flowscited by 11
  11. 2021Implicit Riemannian Concave Potential Mapscited by 10
  12. 2024Ensembles provably learn equivariance through data augmentationcited by 8
8 more
  1. 2022Grassmann Manifold Flows for Stable Shape Generationcited by 3
  2. 2024Equivariant Manifold Neural ODEs and Differential Invariantscited by 2
  3. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  4. 2023Conformal Generative Modeling on Triangulated Surfacescited by 1
  5. 2026EquiDexFlow: Contact-Grounded SE(3)-Equivariant Dexterous Grasp Generative Flowscited by 1
  6. 2025Normalizing Flows on Quotient Manifolds via Boundary Quotientscited by 0
  7. 2026Steerable Neural ODEs on Homogeneous Spacescited by 0
  8. 2026Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Predictioncited by 0