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Wasserstein-2 Generative Networks

arXiv 1909.13082 ↗First posted 28 Sep 2019cs.LG cs.CV stat.MLcited by 96

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Abstract (arXiv)

We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to approximate Wasserstein-2 distance. In contrast to popular entropic and quadratic regularizers, cycle-consistency does not introduce bias and scales well to high dimensions. From the theoretical side, we estimate the properties of the generative mapping fitted by our algorithm. From the practical side, we evaluate our algorithm on a wide range of tasks: image-to-image color transfer, latent space optimal transport, image-to-image style transfer, and domain adaptation.

Key facts. Cited by 96 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Sep 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 15; 2022: 14; 2023: 24; 2024: 16; 2025: 21; 2026: 6.

96 papers.

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  1. 2022Neural Optimal Transportcited by 123
  2. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  3. 2022Tutorial on amortized optimizationcited by 83
  4. 2025ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learningcited by 83
  5. 2021Generative Modeling with Optimal Transport Mapscited by 80
  6. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  7. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  8. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  9. 2022Supervised Training of Conditional Monge Mapscited by 60
  10. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 59
  11. 2021Variational Wasserstein gradient flowcited by 53
  12. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
38 more
  1. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  2. 2021Neural Monge Map estimation and its applicationscited by 40
  3. 2022Normalizing flow neural networks by JKO schemecited by 39
  4. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39
  5. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  6. 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Modelscited by 33
  7. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  8. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  9. 2022Kernel Neural Optimal Transportcited by 31
  10. 2022On amortizing convex conjugates for optimal transportcited by 30
  11. 2022Meta Optimal Transportcited by 28
  12. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  13. 2022Towards Explaining Distribution Shiftscited by 26
  14. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  15. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  16. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  17. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  18. 2023Light Schr"odinger Bridgecited by 18
  19. 2021Input Convex Gradient Networkscited by 17
  20. 2021Riemannian Convex Potential Mapscited by 16
  21. 2022Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplingscited by 16
  22. 2023Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Mapscited by 16
  23. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  24. 2023Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restorationcited by 15
  25. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  26. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  27. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  28. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
  29. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  30. 2023Computing high-dimensional optimal transport by flow neural networkscited by 8
  31. 2024Rethinking Optimal Transport in Offline Reinforcement Learningcited by 8
  32. 2021Understanding Entropic Regularization in GANscited by 6
  33. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  34. 2023Learning Elastic Costs to Shape Monge Displacementscited by 6
  35. 2023Conditional Perceptual Quality Preserving Image Compressioncited by 6
  36. 2024ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transportcited by 6
  37. 2025Convexity in ReLU Neural Networks: beyond ICNNs?cited by 6
  38. 2025Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plancited by 6

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