mlsanityData to 14 Oct 2026

Kernel Neural Optimal Transport

arXiv 2205.15269 ↗First posted 30 May 2022cs.LG stat.MLcited by 31

Not on the map. Why?

Abstract (arXiv)

We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To resolve this issue, we introduce kernel weak quadratic costs. We show that they provide improved theoretical guarantees and practical performance. We test NOT with kernel costs on the unpaired image-to-image translation task.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 35 of its 67 references that are in the map. First posted on arXiv 30 May 2022.

Builds on

35 of 67 references.

References · 35

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  4. 2017Improved Training of Wasserstein GANscited by 2,235
  5. 2013Describing Textures in the Wildcited by 2,125
  6. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  7. 2018Multimodal Unsupervised Image-to-Image Translationcited by 795
  8. 2018Computational Optimal Transportcited by 780
  9. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 464
  10. 2016Input Convex Neural Networkscited by 414
  11. 2019Optimal transport mapping via input convex neural networkscited by 206
  12. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
23 more
  1. 2022Neural Optimal Transportcited by 126
  2. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 123
  3. 2019Wasserstein-2 Generative Networkscited by 97
  4. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 96
  5. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 93
  6. 2020Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimizationcited by 90
  7. 2021Generative Modeling with Optimal Transport Mapscited by 82
  8. 2021Large-Scale Wasserstein Gradient Flowscited by 77
  9. 2018Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Datacited by 76
  10. 2017On the regularization of Wasserstein GANscited by 65
  11. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 60
  12. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  13. 2021Variational Wasserstein gradient flowcited by 53
  14. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  15. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 51
  16. 20192-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANscited by 33
  17. 2019On Scalable and Efficient Computation of Large Scale Optimal Transportcited by 29
  18. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  19. 2018Existence, Duality, and Cyclical monotonicity for weak transport costscited by 21
  20. 2020Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistencycited by 14
  21. 2022An Optimal Transport Perspective on Unpaired Image Super-Resolutioncited by 12
  22. 2019(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithmcited by 11
  23. 2022GAN Estimation of Lipschitz Optimal Transport Mapscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 10; 2024: 7; 2025: 10; 2026: 2.

31 papers.

Sort:

By area:

  1. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  2. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 78
  3. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 50
  4. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  5. 2023Conditional Optimal Transport on Function Spacescited by 26
  6. 2024Degradation-Aware Residual-Conditioned Optimal Transport for Unified Image Restorationcited by 21
  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. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  11. 2024Residual-Conditioned Optimal Transport: Towards Structure-Preserving Unpaired and Paired Image Restorationcited by 13
  12. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
19 more
  1. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  2. 2023Optimal Transport-Guided Conditional Score-Based Diffusion Modelscited by 11
  3. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  4. 2024Rethinking Optimal Transport in Offline Reinforcement Learningcited by 9
  5. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  6. 2023Light Unbalanced Optimal Transportcited by 8
  7. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  8. 2024ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transportcited by 6
  9. 2025Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plancited by 6
  10. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  11. 2025Neural Conditional Transport Mapscited by 2
  12. 2025Towards Prospective Medical Image Reconstruction via Knowledge-Informed Dynamic Optimal Transportcited by 1
  13. 2025Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transportcited by 1
  14. 2025LEHA-CVQAD: Dataset To Enable Generalized Video Quality Assessment of Compression Artifactscited by 1
  15. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  16. 2025Estimation of Stochastic Optimal Transport Mapscited by 1
  17. 2025Universal Representation of Generalized Convex Functions and their Gradientscited by 0
  18. 2026Two-Stage Cross-Domain Cervical Abnormality Screening with Cytopathological Image Synthesis and Knowledge Distillationcited by 0
  19. 2026Simultaneous Neural Optimal Transportcited by 0