mlsanityData to 7 Oct 2026

Computational Optimal Transport

arXiv 1803.00567 ↗First posted 1 Mar 2018stat.MLcited by 765

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Cited by 47 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the worker is to erect with all that sand a target pile with a prescribed shape (for example, that of a giant sand castle). Naturally, the worker wishes to minimize her total effort, quantified for instance as the total distance or time spent carrying shovelfuls of sand. Mathematicians interested in OT cast that problem as that of comparing two probability distributions, two different piles of sand of the same volume. They consider all of the many possible ways to morph, transport or reshape the first pile into the second, and associate a "global" cost to every such transport, using the "local" consideration of how much it costs to move a grain of sand from one place to another. Recent years have witnessed the spread of OT in several fields, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.

Key facts. Cited by 765 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Mar 2018.

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Citing papers per year: 2019: 1; 2020: 3; 2021: 126; 2022: 122; 2023: 138; 2024: 119; 2025: 118; 2026: 138.

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  1. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  2. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  3. 2023LightGlue: Local Feature Matching at Light Speedcited by 583
  4. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  5. 2022Unified Scaling Laws for Routed Language Modelscited by 249
  6. 2022Riemannian Score-Based Generative Modellingcited by 216
  7. 2023Large-scale Multi-Modal Pre-trained Models: A Comprehensive Surveycited by 153
  8. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  9. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  10. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  11. 2022Neural Optimal Transportcited by 123
  12. 2020Primal Wasserstein Imitation Learningcited by 120
38 more
  1. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  2. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  3. 2021Voice2Series: Reprogramming Acoustic Models for Time Series Classificationcited by 91
  4. 2021Entropic estimation of optimal transport mapscited by 87
  5. 2021Class-agnostic Object Detection with Multi-modal Transformercited by 85
  6. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  7. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  8. 2021Low-Rank Sinkhorn Factorizationcited by 66
  9. 2022PLOT: Prompt Learning with Optimal Transport for Vision-Language Modelscited by 64
  10. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  11. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  12. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  13. 2021A Prototype-Oriented Framework for Unsupervised Domain Adaptationcited by 62
  14. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  15. 2022Supervised Training of Conditional Monge Mapscited by 60
  16. 2019Wasserstein Adversarial Imitation Learningcited by 59
  17. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  18. 2024Controlling Language and Diffusion Models by Transporting Activationscited by 59
  19. 2021JointGT: Graph-Text Joint Representation Learning for Text Generation from Knowledge Graphscited by 58
  20. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  21. 2023Posterior Collapse and Latent Variable Non-identifiabilitycited by 57
  22. 2021Don't Generate Me: Training Differentially Private Generative Models with Sinkhorn Divergencecited by 54
  23. 2024Affordance-based Robot Manipulation with Flow Matchingcited by 54
  24. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
  25. 2022MVSTER: Epipolar Transformer for Efficient Multi-View Stereocited by 50
  26. 2021A Primer on Pretrained Multilingual Language Modelscited by 49
  27. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  28. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  29. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  30. 2024Light and Optimal Schr"odinger Bridge Matchingcited by 45
  31. 2021MICo: Improved representations via sampling-based state similarity for Markov decision processescited by 43
  32. 2022Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrumcited by 43
  33. 2023Optimal Transport for Offline Imitation Learningcited by 42
  34. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 41
  35. 2021Adversarial Intrinsic Motivation for Reinforcement Learningcited by 40
  36. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  37. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  38. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39

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