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Learning with minibatch Wasserstein : asymptotic and gradient properties

arXiv 1910.04091 ↗First posted 9 Oct 2019stat.ML cs.LGcited by 83

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Abstract (arXiv)

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this challenge, practitioners compute these distances on minibatches em i.e. they average the outcome of several smaller optimal transport problems. We propose in this paper an analysis of this practice, which effects are not well understood so far. We notably argue that it is equivalent to an implicit regularization of the original problem, with appealing properties such as unbiased estimators, gradients and a concentration bound around the expectation, but also with defects such as loss of distance property. Along with this theoretical analysis, we also conduct empirical experiments on gradient flows, GANs or color transfer that highlight the practical interest of this strategy.

Key facts. Cited by 83 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Oct 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 16; 2023: 17; 2024: 11; 2025: 15; 2026: 11.

83 papers.

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  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. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  4. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  5. 2022FLamby: Datasets and Benchmarks for Cross-Silo Federated Learning in Realistic Healthcare Settingscited by 121
  6. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  7. 2021Generative Modeling with Optimal Transport Mapscited by 80
  8. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  9. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  10. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  11. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  12. 2021MICo: Improved representations via sampling-based state similarity for Markov decision processescited by 43
38 more
  1. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  2. 2024Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generationcited by 36
  3. 2021Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)cited by 33
  4. 2022Spherical Sliced-Wassersteincited by 31
  5. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  6. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  7. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  8. 2021Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddingscited by 19
  9. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  10. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
  11. 2023Light Schr"odinger Bridgecited by 18
  12. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  13. 2025Curly Flow Matching for Learning Non-gradient Field Dynamicscited by 17
  14. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  15. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  16. 2021k-Mixup Regularization for Deep Learning via Optimal Transportcited by 14
  17. 2022Modeling Multimodal Aleatoric Uncertainty in Segmentation with Mixture of Stochastic Expertscited by 13
  18. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  19. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  20. 2023Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Spacecited by 12
  21. 2024Adversarial Schr"odinger Bridge Matchingcited by 12
  22. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  23. 2025Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Pointscited by 11
  24. 2024Revisiting Deep Audio-Text Retrieval Through the Lens of Transportationcited by 10
  25. 2025On Fitting Flow Models with Large Sinkhorn Couplingscited by 10
  26. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  27. 2023Light Unbalanced Optimal Transportcited by 8
  28. 2024Neural Sinkhorn Gradient Flowcited by 8
  29. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
  30. 2025Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Datacited by 8
  31. 2025Differentiable Generalized Sliced Wasserstein Planscited by 7
  32. 2023Consistent Optimal Transport with Empirical Conditional Measurescited by 6
  33. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplingscited by 6
  34. 2022Partial Wasserstein Adversarial Network for Non-rigid Point Set Registrationcited by 5
  35. 2021Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distancecited by 4
  36. 2022Estimating Regression Predictive Distributions with Sample Networkscited by 4
  37. 2024Switched Flow Matching: Eliminating Singularities via Switching ODEscited by 4
  38. 2024Submodular Framework for Structured-Sparse Optimal Transportcited by 4

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