mlsanityData to 7 Oct 2026

Extremal Domain Translation with Neural Optimal Transport

arXiv 2301.12874 ↗First posted 30 Jan 2023cs.LGcited by 12

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Abstract (arXiv)

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical formalization of the theoretically best possible unpaired translation between a pair of domains w.r.t. the given similarity function. Inspired by the recent advances in neural optimal transport (OT), we propose a scalable algorithm to approximate ET maps as a limit of partial OT maps. We test our algorithm on toy examples and on the unpaired image-to-image translation task. The code is publicly available at https://github.com/milenagazdieva/ExtremalNeuralOptimalTransport

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 47 of its 78 references that are in the map. First posted on arXiv 30 Jan 2023.

Builds on

47 of 78 references.

References · 47

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35 more
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  9. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
  10. 2019Optimal transport mapping via input convex neural networkscited by 202
  11. 2017Neural Style Transfer: A Reviewcited by 199
  12. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 188
  13. 2018Unsupervised Image Super-Resolution using Cycle-in-Cycle Generative Adversarial Networkscited by 133
  14. 2022Neural Optimal Transportcited by 123
  15. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  16. 2021Image-to-Image Translation: Methods and Applicationscited by 116
  17. 2019Wasserstein-2 Generative Networkscited by 96
  18. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  19. 2020Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptationcited by 86
  20. 2021Generative Modeling with Optimal Transport Mapscited by 80
  21. 2021Real-World Single Image Super-Resolution: A Brief Reviewcited by 65
  22. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 59
  23. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  24. 2020Outlier-Robust Optimal Transportcited by 45
  25. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 41
  26. 2021Neural Monge Map estimation and its applicationscited by 40
  27. 2022Neural Optimal Transport with General Cost Functionalscited by 34
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  30. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  31. 2022Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplingscited by 16
  32. 2022An Optimal Transport Perspective on Unpaired Image Super-Resolutioncited by 12
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 5; 2025: 2; 2026: 2.

12 papers.

  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  2. 2023Light Schr"odinger Bridgecited by 18
  3. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  4. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  5. 2023Light Unbalanced Optimal Transportcited by 8
  6. 2024Rethinking Optimal Transport in Offline Reinforcement Learningcited by 8
  7. 2024ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transportcited by 6
  8. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  9. 2024Optimal Transport Maps are Good Voice Converterscited by 4
  10. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  11. 2026Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspectivecited by 0
  12. 2026Simultaneous Neural Optimal Transportcited by 0