mlsanityData to 7 Oct 2026

Entropic Neural Optimal Transport via Diffusion Processes

arXiv 2211.01156 ↗First posted 2 Nov 2022cs.LGcited by 49

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Abstract (arXiv)

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schr"odinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks. https://github.com/ngushchin/EntropicNeuralOptimalTransport

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Builds on 37 of its 60 references that are in the map. First posted on arXiv 2 Nov 2022.

Builds on

37 of 60 references.

References · 37

  1. 2014Going Deeper with Convolutionscited by 4,231
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2018Multimodal Unsupervised Image-to-Image Translationcited by 795
  5. 2018Computational Optimal Transportcited by 765
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  7. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
  8. 2016Input Convex Neural Networkscited by 407
  9. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  10. 2013Fast Computation of Wasserstein Barycenterscited by 216
  11. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  12. 2019Optimal transport mapping via input convex neural networkscited by 202
25 more
  1. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  2. 2022Neural Optimal Transportcited by 123
  3. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  4. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  5. 2019Wasserstein-2 Generative Networkscited by 96
  6. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  7. 2021Generative Modeling with Optimal Transport Mapscited by 80
  8. 2018Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Datacited by 76
  9. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  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
  13. 2022Deep Generalized Schr"odinger Bridgecited by 47
  14. 2021Neural Monge Map estimation and its applicationscited by 40
  15. 2020Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Gamescited by 35
  16. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  17. 2022Kernel Neural Optimal Transportcited by 31
  18. 2022On amortizing convex conjugates for optimal transportcited by 30
  19. 2019On Scalable and Efficient Computation of Large Scale Optimal Transportcited by 29
  20. 2018Existence, Duality, and Cyclical monotonicity for weak transport costscited by 21
  21. 2019Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transportcited by 19
  22. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  23. 2020Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistencycited by 14
  24. 2019(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithmcited by 11
  25. 2022Algorithms for Weak Optimal Transport with an Application to Economicscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 12; 2024: 13; 2025: 19; 2026: 5.

49 papers.

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  1. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  2. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  3. 2024Light and Optimal Schr"odinger Bridge Matchingcited by 45
  4. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  5. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  6. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  7. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  8. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  9. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  10. 2023Light Schr"odinger Bridgecited by 18
  11. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  12. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
37 more
  1. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  2. 2024Adversarial Schr"odinger Bridge Matchingcited by 12
  3. 2024Schr"odinger Bridge with Quadratic State Cost is Exactly Solvablecited by 12
  4. 2025Trajectory Inference with Smooth Schr"odinger Bridgescited by 10
  5. 2024Diffusion & Adversarial Schr"odinger Bridges via Iterative Proportional Markovian Fittingcited by 9
  6. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  7. 2023Light Unbalanced Optimal Transportcited by 8
  8. 2025InfoBridge: Mutual Information estimation via Bridge Matchingcited by 7
  9. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  10. 2025Field Matching: an Electrostatic Paradigm to Generate and Transfer Datacited by 6
  11. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  12. 2024Scalable Simulation-free Entropic Unbalanced Optimal Transportcited by 5
  13. 2025Categorical Schr"odinger Bridge Matchingcited by 5
  14. 2025MixBridge: Heterogeneous Image-to-Image Backdoor Attack through Mixture of Schr"odinger Bridgescited by 5
  15. 2025Interaction Field Matching: Overcoming Limitations of Electrostatic Modelscited by 4
  16. 2025Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)cited by 4
  17. 2025Improved Stochastic Optimization of LogSumExpcited by 4
  18. 2024Conditional Lagrangian Wasserstein Flow for Time Series Imputationcited by 3
  19. 2025Universal Vessel Segmentation for Multi-Modality Retinal Imagescited by 3
  20. 2024Neural Shr"odinger Bridge Matching for Pansharpeningcited by 2
  21. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  22. 2024Generative Conditional Distributions by Neural (Entropic) Optimal Transportcited by 1
  23. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  24. 2025CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshotscited by 1
  25. 2025Weighted Conditional Flow Matchingcited by 1
  26. 2025Incorporating Pre-trained Diffusion Models in Solving the Schr"odinger Bridge Problemcited by 1
  27. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  28. 2025Experts-Guided Unbalanced Optimal Transport for ISP Learning from Unpaired and/or Paired Datacited by 1
  29. 2026Variational Entropic Optimal Transportcited by 1
  30. 2023Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transportcited by 0
  31. 2024Regularized Distribution Matching Distillation for One-step Unpaired Image-to-Image Translationcited by 0
  32. 2024Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximizationcited by 0
  33. 2025Entering the Era of Discrete Diffusion Models: A Benchmark for Schr"odinger Bridges and Entropic Optimal Transportcited by 0
  34. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0
  35. 2026A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solutioncited by 0
  36. 2026Di2CycleSB: Towards High-Quality Unsupervised Nighttime Visibility Enhancement via Schr"odinger Bridge Transformercited by 0
  37. 2026Tilted Schr"odinger Bridge Matchingcited by 0