mlsanityData to 7 Oct 2026

Neural Optimal Transport

arXiv 2201.12220 ↗First posted 28 Jan 2022cs.LGcited by 123

Not on the map. Why?

Abstract (arXiv)

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions. We evaluate the performance of our optimal transport algorithm on toy examples and on the unpaired image-to-image translation.

Key facts. Cited by 123 papers in the map (data through 7 Oct 2026). Builds on 40 of its 69 references that are in the map. First posted on arXiv 28 Jan 2022.

Builds on

40 of 69 references.

References · 40

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  5. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,678
  6. 2017Improved Training of Wasserstein GANscited by 2,223
  7. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  8. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  9. 2018Multimodal Unsupervised Image-to-Image Translationcited by 795
  10. 2018Computational Optimal Transportcited by 765
  11. 2017Unsupervised Image-to-Image Translation Networkscited by 602
  12. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
28 more
  1. 2016Input Convex Neural Networkscited by 407
  2. 2017Toward Multimodal Image-to-Image Translationcited by 295
  3. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  4. 2017Learning to Discover Cross-Domain Relations with Generative Adversarial Networkscited by 278
  5. 2019Optimal transport mapping via input convex neural networkscited by 202
  6. 2019Universal Approximation with Deep Narrow Networkscited by 198
  7. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 188
  8. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  9. 2019Wasserstein-2 Generative Networkscited by 96
  10. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  11. 2017One-Sided Unsupervised Domain Mappingcited by 91
  12. 2021Generative Modeling with Optimal Transport Mapscited by 80
  13. 2018Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Datacited by 76
  14. 2017On the regularization of Wasserstein GANscited by 65
  15. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 59
  16. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  17. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
  18. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 49
  19. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 41
  20. 2020COCO-FUNIT: Few-Shot Unsupervised Image Translation with a Content Conditioned Style Encodercited by 39
  21. 20192-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANscited by 32
  22. 2019On Scalable and Efficient Computation of Large Scale Optimal Transportcited by 29
  23. 2018Sem-GAN: Semantically-Consistent Image-to-Image Translationcited by 26
  24. 2018Existence, Duality, and Cyclical monotonicity for weak transport costscited by 21
  25. 2020Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistencycited by 14
  26. 2020GMM-UNIT: Unsupervised Multi-Domain and Multi-Modal Image-to-Image Translation via Attribute Gaussian Mixture Modelingcited by 11
  27. 2018Guiding the One-to-one Mapping in CycleGAN via Optimal Transportcited by 6
  28. 2018XOGAN: One-to-Many Unsupervised Image-to-Image Translationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 11; 2023: 23; 2024: 28; 2025: 34; 2026: 27.

123 papers.

Sort:

By area:

  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  2. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  3. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  4. 2022Dual Diffusion Implicit Bridges for Image-to-Image Translationcited by 212
  5. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  6. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  7. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  8. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  9. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39
  10. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  11. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  12. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
38 more
  1. 2022Kernel Neural Optimal Transportcited by 31
  2. 2022Meta Optimal Transportcited by 28
  3. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  4. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  5. 2024Degradation-Aware Residual-Conditioned Optimal Transport for Unified Image Restorationcited by 21
  6. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  7. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  8. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  9. 2023Light Schr"odinger Bridgecited by 18
  10. 2023Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restorationcited by 15
  11. 2025On the Relation between Rectified Flows and Optimal Transportcited by 15
  12. 2023Comparing the Robustness of Modern No-Reference Image- and Video-Quality Metrics to Adversarial Attackscited by 14
  13. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  14. 2024Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformerscited by 14
  15. 2024Residual-Conditioned Optimal Transport: Towards Structure-Preserving Unpaired and Paired Image Restorationcited by 13
  16. 2022An Optimal Transport Perspective on Unpaired Image Super-Resolutioncited by 12
  17. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  18. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  19. 2023Optimal Transport-Guided Conditional Score-Based Diffusion Modelscited by 11
  20. 2024Context-Aware Optimal Transport Learning for Retinal Fundus Image Enhancementcited by 10
  21. 2023Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernelscited by 9
  22. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  23. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  24. 2023Computing high-dimensional optimal transport by flow neural networkscited by 8
  25. 2023Analyzing and Improving Optimal-Transport-based Adversarial Networkscited by 8
  26. 2024Rethinking Optimal Transport in Offline Reinforcement Learningcited by 8
  27. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
  28. 2024Align Your Intents: Offline Imitation Learning via Optimal Transportcited by 7
  29. 2024Improving Neural Optimal Transport via Displacement Interpolationcited by 7
  30. 2025Distributional Vision-Language Alignment by Cauchy-Schwarz Divergencecited by 7
  31. 2022Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flowscited by 6
  32. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  33. 2023Consistent Optimal Transport with Empirical Conditional Measurescited by 6
  34. 2024ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transportcited by 6
  35. 2025Convexity in ReLU Neural Networks: beyond ICNNs?cited by 6
  36. 2025Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plancited by 6
  37. 2025Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpeningcited by 6
  38. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6

50 most cited of 123 All 123 (JSON)