mlsanityData to 14 Oct 2026

Neural Optimal Transport with General Cost Functionals

arXiv 2205.15403 ↗First posted 30 May 2022cs.LGcited by 36

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Abstract (arXiv)

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ℓ1 or ℓ2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Builds on 60 of its 96 references that are in the map. First posted on arXiv 30 May 2022.

Builds on

60 of 96 references.

References · 60

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38 more
  1. 2018Computational Optimal Transportcited by 780
  2. 2018Deep Visual Domain Adaptation: A Surveycited by 635
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  5. 2017Unsupervised Image-to-Image Translation Networkscited by 603
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  7. 2015Optimal Transport for Domain Adaptationcited by 463
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  11. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 282
  12. 2018DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptationcited by 214
  13. 2022Dual Diffusion Implicit Bridges for Image-to-Image Translationcited by 213
  14. 2019Optimal transport mapping via input convex neural networkscited by 206
  15. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
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  20. 2019Wasserstein-2 Generative Networkscited by 97
  21. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 96
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  23. 2020Deep Visual Domain Adaptationcited by 91
  24. 2021Entropic estimation of optimal transport mapscited by 90
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Citing papers per year: 2022: 3; 2023: 13; 2024: 6; 2025: 8; 2026: 6.

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  1. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 278
  2. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 78
  3. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 50
  4. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  5. 2022On amortizing convex conjugates for optimal transportcited by 31
  6. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  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. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  12. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
24 more
  1. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  2. 2024Rethinking Optimal Transport in Offline Reinforcement Learningcited by 9
  3. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  4. 2023Light Unbalanced Optimal Transportcited by 8
  5. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  6. 2025Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpeningcited by 6
  7. 2023Generating Synthetic Datasets by Interpolating along Generalized Geodesicscited by 5
  8. 2024Optimal Transport Maps are Good Voice Converterscited by 4
  9. 2025Improved Stochastic Optimization of LogSumExpcited by 4
  10. 2023Semi-supervised Learning of Pushforwards For Domain Translation & Adaptationcited by 2
  11. 2023OT-Net: A Reusable Neural Optimal Transport Solvercited by 2
  12. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  13. 2023Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applicationscited by 1
  14. 2025Displacement-Sparse Neural Optimal Transportcited by 1
  15. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  16. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  17. 2025Expert or not? assessing data quality in offline reinforcement learningcited by 1
  18. 2024Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximizationcited by 0
  19. 2026Hyperparameter Trajectory Inference with Conditional Lagrangian Optimal Transportcited by 0
  20. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0
  21. 2026Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact p-Wasserstein Dynamicscited by 0
  22. 2026Conformal Risk Minimization for Semi-Supervised Domain Adaptation via Optimal Transportcited by 0
  23. 2026Light Entropic Optimal Transport on Riemannian Manifoldscited by 0
  24. 2026Scaling Online Optimal Transport Minibatches for Flow Matchingcited by 0