mlsanityData to 14 Oct 2026

Neural Monge Map estimation and its applications

arXiv 2106.03812 ↗First posted 7 Jun 2021cs.LG math.OCcited by 40

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Abstract (arXiv)

Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network based optimal transport map solver has gained great attention in recent years. Along this line, we present a scalable algorithm for computing the neural Monge map between two probability distributions. Our algorithm is based on a weak form of the optimal transport problem, thus it only requires samples from the marginals instead of their analytic expressions, and can accommodate optimal transport between two distributions with different dimensions. Our algorithm is suitable for general cost functions, compared with other existing methods for estimating Monge maps using samples, which are usually for quadratic costs. The performance of our algorithms is demonstrated through a series of experiments with both synthetic and realistic data, including text-to-image generation and image inpainting tasks.

Key facts. Cited by 40 papers in the map (data through 14 Oct 2026). Builds on 34 of its 84 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

34 of 84 references.

References · 34

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  4. 2021Zero-Shot Text-to-Image Generationcited by 4,288
  5. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  6. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  7. 2017Improved Training of Wasserstein GANscited by 2,235
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  9. 2015Optimal Transport for Domain Adaptationcited by 463
  10. 2018Deep Learning for Classical Japanese Literaturecited by 422
  11. 2016Input Convex Neural Networkscited by 414
  12. 2017Learning Generative Models with Sinkhorn Divergencescited by 314
22 more
  1. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 282
  2. 2018cGANs with Projection Discriminatorcited by 254
  3. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 223
  4. 2018Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learningcited by 215
  5. 2019Optimal transport mapping via input convex neural networkscited by 206
  6. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
  7. 2020Geometric Dataset Distances via Optimal Transportcited by 158
  8. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 123
  9. 2019Wasserstein-2 Generative Networkscited by 97
  10. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 96
  11. 2021Large-Scale Wasserstein Gradient Flowscited by 77
  12. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  13. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 51
  14. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 50
  15. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 42
  16. 2020SpinalNet: Deep Neural Network with Gradual Inputcited by 40
  17. 2018Learning to Match via Inverse Optimal Transportcited by 23
  18. 2020Multi-marginal optimal transport and probabilistic graphical modelscited by 13
  19. 2020Learning Stochastic Behaviour from Aggregate Datacited by 12
  20. 2020Optimal Transport-based Coverage Control for Swarm Robot Systems: Generalization of the Voronoi Tessellation-based Methodcited by 7
  21. 2021Functional optimal transport: map estimation and domain adaptation for functional datacited by 7
  22. 2018Optimal transportation between unequal dimensionscited by 6

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Citing papers per year: 2022: 4; 2023: 9; 2024: 9; 2025: 9; 2026: 9.

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  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 78
  2. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 50
  3. 2022Neural Optimal Transport with General Cost Functionalscited by 36
  4. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  5. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  6. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  7. 2023Light Schr"odinger Bridgecited by 18
  8. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  9. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  10. 2022An Optimal Transport Perspective on Unpaired Image Super-Resolutioncited by 12
  11. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  12. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
28 more
  1. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  2. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 9
  3. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  4. 2023Light Unbalanced Optimal Transportcited by 8
  5. 2023Computing high-dimensional optimal transport by flow neural networkscited by 8
  6. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  7. 2025Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plancited by 6
  8. 2023Generating Synthetic Datasets by Interpolating along Generalized Geodesicscited by 5
  9. 2024Differentiable Cost-Parameterized Monge Map Estimatorscited by 2
  10. 2024A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equationscited by 2
  11. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  12. 2024Unsupervised Point Cloud Completion through Unbalanced Optimal Transportcited by 1
  13. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  14. 2025DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guaranteecited by 1
  15. 2025Reweighted Flow Matching via Unbalanced OT for Label-free Long-tailed Generationcited by 1
  16. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  17. 2026Rate-Optimal Noise Annealing in Semi-Dual Neural Optimal Transport: Tangential Identifiability, Off-Manifold Ambiguity, and Guaranteed Recoverycited by 1
  18. 2024Strongly Isomorphic Neural Optimal Transport Across Incomparable Spacescited by 0
  19. 2024Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Mapscited by 0
  20. 2025COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networkscited by 0
  21. 2026Neural Optimal Transport in Hilbert Spaces: Characterizing Spurious Solutions and Gaussian Smoothingcited by 0
  22. 2026Neural solver for Wasserstein Geodesics and optimal transport dynamicscited by 0
  23. 2026Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modelingcited by 0
  24. 2026Stability of the Monge Map in Semi-Dual Optimal Transportcited by 0
  25. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0
  26. 2026UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problemscited by 0
  27. 2026Deep Barycentric Regression for Optimal Transport Map Estimation and its Statistical Optimalitycited by 0
  28. 2026Simultaneous Neural Optimal Transportcited by 0