mlsanityData to 7 Oct 2026

Learning normalizing flows from Entropy-Kantorovich potentials

arXiv 2006.06033 ↗First posted 10 Jun 2020cs.LG stat.MLcited by 18

Not on the map. Why?

Abstract (arXiv)

We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This formulation allows us to train a dual objective comprised only of the scalar potential functions, and removes the burden of explicitly computing normalizing flows during training. After training, the normalizing flow is easily recovered from the potential functions.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jun 2020.

Builds on

No reference list yet.

Built on by

Cited by year

Citing papers per year: 2021: 4; 2022: 2; 2023: 6; 2024: 4; 2025: 2.

18 papers.

Sort:

By area:

  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  2. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  3. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  4. 2021Entropic estimation of optimal transport mapscited by 87
  5. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  6. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  7. 2022Optimal transport map estimation in general function spacescited by 20
  8. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  9. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  10. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  11. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  12. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
6 more
  1. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  2. 2022Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flowscited by 6
  3. 2024Scalable Simulation-free Entropic Unbalanced Optimal Transportcited by 5
  4. 2025Devil is in the Details: Density Guidance for Detail-Aware Generation with Flow Modelscited by 5
  5. 2024Simplified Diffusion Schr"odinger Bridgecited by 4
  6. 2023Normalizing flows as approximations of optimal transport maps via linear-control neural ODEscited by 2