mlsanityData to 7 Oct 2026

Minibatch optimal transport distances; analysis and applications

arXiv 2101.01792 ↗First posted 5 Jan 2021stat.ML cs.LGcited by 62

Not on the map. Why?

Cited by 22 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on large scale datasets. To overcome this challenge, a common workaround is to compute these distances on minibatches i.e. to average the outcome of several smaller optimal transport problems. We propose in this paper an extended analysis of this practice, which effects were previously studied in restricted cases. We first consider a large variety of Optimal Transport kernels. We notably argue that the minibatch strategy comes with appealing properties such as unbiased estimators, gradients and a concentration bound around the expectation, but also with limits: the minibatch OT is not a distance. To recover some of the lost distance axioms, we introduce a debiased minibatch OT function and study its statistical and optimisation properties. Along with this theoretical analysis, we also conduct empirical experiments on gradient flows, generative adversarial networks (GANs) or color transfer that highlight the practical interest of this strategy.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). Builds on 42 of its 80 references that are in the map. First posted on arXiv 5 Jan 2021.

Builds on

42 of 80 references.

References · 42

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2013Auto-Encoding Variational Bayescited by 3,980
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  5. 2017Improved Training of Wasserstein GANscited by 2,223
  6. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  7. 2018Demystifying MMD GANscited by 1,268
  8. 2018Computational Optimal Transportcited by 765
  9. 2015Optimal Transport for Domain Adaptationcited by 457
  10. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  11. 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
  12. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
30 more
  1. 2018DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptationcited by 212
  2. 2019Generalized Sliced Wasserstein Distancescited by 205
  3. 2015Learning with a Wasserstein Losscited by 194
  4. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 188
  5. 2013Minimizing Finite Sums with the Stochastic Average Gradientcited by 164
  6. 2018Improving GANs Using Optimal Transportcited by 122
  7. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  8. 2018Stochastic subgradient method converges on tame functionscited by 120
  9. 2017The Cramer Distance as a Solution to Biased Wasserstein Gradientscited by 116
  10. 2019A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Normcited by 105
  11. 2019Wasserstein Adversarial Examples via Projected Sinkhorn Iterationscited by 89
  12. 2017Smooth and Sparse Optimal Transportcited by 83
  13. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  14. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
  15. 2019Sliced Gromov-Wassersteincited by 66
  16. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 64
  17. 2019Sliced Wasserstein Generative Modelscited by 61
  18. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  19. 2019Tree-Sliced Variants of Wasserstein Distancescited by 54
  20. 2019Learning Generative Models across Incomparable Spacescited by 53
  21. 2019Hierarchical Optimal Transport for Multimodal Distribution Alignmentcited by 38
  22. 2018Towards Optimal Transport with Global Invariancescited by 33
  23. 2020Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimizationcited by 32
  24. 2018Optimal Transport: Fast Probabilistic Approximation with Exact Solverscited by 27
  25. 2016Regularized Optimal Transport and the Rot Mover's Distancecited by 24
  26. 2018Analysis of nonsmooth stochastic approximation: the differential inclusion approachcited by 21
  27. 2017Multiscale Strategies for Computing Optimal Transportcited by 18
  28. 2015Scaling-up Empirical Risk Minimization: Optimization of Incomplete U-statisticscited by 17
  29. 2018Greedy stochastic algorithms for entropy-regularized optimal transport problemscited by 9
  30. 2020Stochastic Optimization for Regularized Wasserstein Estimatorscited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 9; 2023: 14; 2024: 6; 2025: 15; 2026: 10.

62 papers.

Sort:

By area:

  1. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  2. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  3. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  4. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  5. 2023Equivariant flow matchingcited by 131
  6. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  7. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  8. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  9. 2021MICo: Improved representations via sampling-based state similarity for Markov decision processescited by 43
  10. 2024Categorical Flow Matching on Statistical Manifoldscited by 43
  11. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  12. 2024Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generationcited by 36
38 more
  1. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  2. 2022Domain Adaptation for Time-Series Classification to Mitigate Covariate Shiftcited by 24
  3. 2021Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddingscited by 19
  4. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  5. 2021Quantized Gromov-Wassersteincited by 18
  6. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  7. 2025Curly Flow Matching for Learning Non-gradient Field Dynamicscited by 17
  8. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  9. 2023Properties of Discrete Sliced Wasserstein Lossescited by 12
  10. 2023Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Spacecited by 12
  11. 2025Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Pointscited by 11
  12. 2024Improving Molecular Graph Generation with Flow Matching and Optimal Transportcited by 10
  13. 2025Statistical Properties of Rectified Flowcited by 10
  14. 2022Improving Molecular Representation Learning with Metric Learning-enhanced Optimal Transportcited by 9
  15. 2022GeoECG: Data Augmentation via Wasserstein Geodesic Perturbation for Robust Electrocardiogram Predictioncited by 8
  16. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
  17. 2025Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Datacited by 8
  18. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplingscited by 6
  19. 2026Faster Inference of Flow-Based Generative Models via Improved Data-Noise Couplingcited by 6
  20. 2024Minibatch Optimal Transport and Perplexity Bound Estimation in Discrete Flow Matchingcited by 5
  21. 2021Subspace Detours Meet Gromov-Wassersteincited by 4
  22. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  23. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  24. 2024Improving Consistency Models with Generator-Augmented Flowscited by 4
  25. 2025Prompt-OT: An Optimal Transport Regularization Paradigm for Knowledge Preservation in Vision-Language Model Adaptationcited by 4
  26. 2025Inductive Domain Transfer In Misspecified Simulation-Based Inferencecited by 4
  27. 2026Expected Batch Optimal Transport Plans and Consequences for Flow Matchingcited by 4
  28. 2021Training Wasserstein GANs without gradient penaltiescited by 3
  29. 2023Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesicscited by 3
  30. 2024Modeling Stochastic Conditional Dynamics from Sparse Observations via Kernel-Stabilized Flow Matchingcited by 3
  31. 2025Departures: Distributional Transport for Single-Cell Perturbation Prediction with Neural Schr"odinger Bridgescited by 3
  32. 2026Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generationcited by 3
  33. 2022Optimal transport meets noisy label robust loss and MixUp regularization for domain adaptationcited by 2
  34. 2025Distances for Markov chains from sample streamscited by 2
  35. 2025Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schr"odinger Bridgescited by 2
  36. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  37. 2026COT-FM: Cluster-wise Optimal Transport Flow Matchingcited by 2
  38. 2022Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transportcited by 1

50 most cited of 62 All 62 (JSON)