mlsanityData to 7 Oct 2026

Convergence Rates for Distribution Matching with Sliced Optimal Transport

arXiv 2602.10691 ↗First posted 11 Feb 2026stat.ML cs.LGcited by 2

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Abstract (arXiv)

We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish Lojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 39 of its 73 references that are in the map. First posted on arXiv 11 Feb 2026.

Builds on

39 of 73 references.

References · 39

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  4. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 716
  5. 2015Optimal Transport for Domain Adaptationcited by 457
  6. 2023Handbook of Convergence Theorems for (Stochastic) Gradient Methodscited by 158
  7. 2020Better Theory for SGD in the Nonconvex Worldcited by 156
  8. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
  9. 2017Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chainscited by 84
  10. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  11. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
  12. 2019Sliced Wasserstein Generative Modelscited by 61
27 more
  1. 2024Statistical optimal transportcited by 44
  2. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  3. 2018On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradientcited by 42
  4. 2020Sliced Iterative Normalizing Flowscited by 37
  5. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  6. 2019Minimax Confidence Intervals for the Sliced Wasserstein Distancecited by 24
  7. 2023On Sampling with Approximate Transport Mapscited by 20
  8. 2022First-order Conditions for Optimization in the Wasserstein Spacecited by 19
  9. 2024Expected Sliced Transport Planscited by 19
  10. 2022On minimax density estimation via measure transportcited by 18
  11. 2021Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Ratescited by 16
  12. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  13. 2023Properties of Discrete Sliced Wasserstein Lossescited by 12
  14. 2024Mirror and Preconditioned Gradient Descent in Wasserstein Spacecited by 11
  15. 2024Progressive Entropic Optimal Transport Solverscited by 10
  16. 2018A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problemscited by 7
  17. 2024Long-Time Asymptotics of the Sliced-Wasserstein Flowcited by 7
  18. 2025A User's Guide to Sampling Strategies for Sliced Optimal Transportcited by 7
  19. 2022Sliced-Wasserstein normalizing flows: beyond maximum likelihood trainingcited by 6
  20. 2023Measure transfer via stochastic slicing and matchingcited by 6
  21. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  22. 2023Approximation properties of slice-matching operatorscited by 3
  23. 2025Convergence of drift-diffusion PDEs arising as Wasserstein gradient flows of convex functionscited by 3
  24. 2025Sharp comparisons between sliced and standard 1-Wasserstein distancescited by 2
  25. 2023Sliced optimal transport: is it a suitable replacement?cited by 1
  26. 2024A Generalized Version of Chung's Lemma and its Applicationscited by 1
  27. 2024Optimization with First Order Algorithmscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0
  2. 2026Distribution Steering via Sliced Optimal Transport Controlcited by 0