mlsanityData to 7 Oct 2026

Riemannian Continuous Normalizing Flows

arXiv 2006.10605 ↗First posted 18 Jun 2020stat.ML cs.LGcited by 143

Not on the map. Why?

Cited by 43 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic spaces, most normalizing flows implicitly assume a flat geometry, making them either misspecified or ill-suited in these situations. To overcome this problem, we introduce Riemannian continuous normalizing flows, a model which admits the parametrization of flexible probability measures on smooth manifolds by defining flows as the solution to ordinary differential equations. We show that this approach can lead to substantial improvements on both synthetic and real-world data when compared to standard flows or previously introduced projected flows.

Key facts. Cited by 143 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2020.

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Citing papers per year: 2021: 19; 2022: 25; 2023: 20; 2024: 14; 2025: 28; 2026: 37.

143 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2023Flow Matching on General Geometriescited by 260
  3. 2022Riemannian Score-Based Generative Modellingcited by 216
  4. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  5. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  6. 2022Riemannian Diffusion Modelscited by 120
  7. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  8. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  9. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  10. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  11. 2021Closed-form Continuous-time Neural Modelscited by 65
  12. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
38 more
  1. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  2. 2022Matching Normalizing Flows and Probability Paths on Manifoldscited by 57
  3. 2021Smooth Normalizing Flowscited by 52
  4. 2021Rectangular Flows for Manifold Learningcited by 49
  5. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  6. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  7. 2025On the Guidance of Flow Matchingcited by 44
  8. 2024Categorical Flow Matching on Statistical Manifoldscited by 43
  9. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 40
  10. 2022Normalizing flow neural networks by JKO schemecited by 39
  11. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 38
  12. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  13. 2022Spherical Sliced-Wassersteincited by 31
  14. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 30
  15. 2022Diagnosing and Fixing Manifold Overfitting in Deep Generative Modelscited by 28
  16. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  17. 2023Poincar'e ResNetcited by 24
  18. 2023Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processescited by 21
  19. 2023Riemannian Residual Neural Networkscited by 21
  20. 2021Equivariant Manifold Flowscited by 20
  21. 2024Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groupscited by 19
  22. 2022First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Datacited by 18
  23. 2023Scaling Riemannian Diffusion Modelscited by 18
  24. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  25. 2025FARMER: Flow AutoRegressive Transformer over Pixelscited by 17
  26. 2021Riemannian Convex Potential Mapscited by 16
  27. 2023Efficient Training of Energy-Based Models Using Jarzynski Equalitycited by 15
  28. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  29. 2026Language Modeling with Hyperspherical Flowscited by 15
  30. 2022Hyperbolic VAE via Latent Gaussian Distributionscited by 14
  31. 2023Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modelingcited by 14
  32. 2025Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularitycited by 14
  33. 2025Flow Matching Meets Biology and Life Science: A Surveycited by 14
  34. 2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
  35. 2025Carr'e du champ flow matching: better quality-generalisation tradeoff in generative modelscited by 13
  36. 2021Learning Stable Vector Fields on Lie Groupscited by 12
  37. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 12
  38. 2026Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoderscited by 12

50 most cited of 143 All 143 (JSON)