mlsanityData to 14 Oct 2026

Riemannian Convex Potential Maps

arXiv 2106.10272 ↗First posted 18 Jun 2021cs.LG stat.MLcited by 17

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Abstract (arXiv)

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational tradeoffs. We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. These are universal and can model distributions on any compact Riemannian manifold without requiring domain knowledge of the manifold to be integrated into the architecture. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data. Our source code is freely available online at http://github.com/facebookresearch/rcpm

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 21 of its 52 references that are in the map. First posted on arXiv 18 Jun 2021.

Builds on

21 of 52 references.

References · 21

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2015Variational Inference with Normalizing Flowscited by 2,170
  3. 2016Density estimation using Real NVPcited by 2,042
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  5. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  6. 2016Input Convex Neural Networkscited by 414
  7. 2017Soft-DTW: a Differentiable Loss Function for Time-Seriescited by 271
  8. 2019Optimal transport mapping via input convex neural networkscited by 206
  9. 2020Riemannian Continuous Normalizing Flowscited by 145
  10. 2020Flows for simultaneous manifold learning and density estimationcited by 118
  11. 2020Normalizing Flows on Tori and Spherescited by 117
  12. 2019Wasserstein-2 Generative Networkscited by 97
9 more
  1. 2020Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimizationcited by 90
  2. 2020Neural Manifold Ordinary Differential Equationscited by 81
  3. 2018Latent Space Policies for Hierarchical Reinforcement Learningcited by 67
  4. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  5. 2020Latent Variable Modelling with Hyperbolic Normalizing Flowscited by 49
  6. 2019Equivariant Hamiltonian Flowscited by 39
  7. 2020The Expressive Power of a Class of Normalizing Flow Modelscited by 35
  8. 2019Unsupervised Hierarchy Matching with Optimal Transport over Hyperbolic Spacescited by 14
  9. 2020Aligning Hyperbolic Representations: an Optimal Transport-based approachcited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 6; 2023: 5; 2024: 2; 2025: 1; 2026: 1.

17 papers.

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  1. 2022Riemannian Score-Based Generative Modellingcited by 219
  2. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 150
  3. 2022Tutorial on amortized optimizationcited by 83
  4. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  5. 2022Spherical Sliced-Wassersteincited by 31
  6. 2022On amortizing convex conjugates for optimal transportcited by 31
  7. 2022Meta Optimal Transportcited by 28
  8. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  9. 2022Symmetry-Based Representations for Artificial and Biological General Intelligencecited by 26
  10. 2021Implicit Riemannian Concave Potential Mapscited by 10
  11. 2023Learning Elastic Costs to Shape Monge Displacementscited by 6
  12. 2021Transport away your problems: Calibrating stochastic simulations with optimal transportcited by 5
5 more
  1. 2023Vector Quantile Regression on Manifoldscited by 3
  2. 2024On a Neural Implementation of Brenier's Polar Factorizationcited by 3
  3. 2024HOTS3D: Hyper-Spherical Optimal Transport for Semantic Alignment of Text-to-3D Generationcited by 1
  4. 2025GradNetOT: Learning Optimal Transport Maps with GradNetscited by 0
  5. 2026Light Entropic Optimal Transport on Riemannian Manifoldscited by 0