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Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

arXiv 1806.08141 ↗First posted 21 Jun 2018stat.ML cs.LGcited by 77

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Abstract (arXiv)

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes. We formulate the problem as a gradient flow in the space of probability measures. The connections between gradient flows and stochastic differential equations let us develop a computationally efficient algorithm for solving the optimization problem. We provide formal theoretical analysis where we prove finite-time error guarantees for the proposed algorithm. To the best of our knowledge, the proposed algorithm is the first nonparametric IGM algorithm with explicit theoretical guarantees. Our experimental results support our theory and show that our algorithm is able to successfully capture the structure of different types of data distributions.

Key facts. Cited by 77 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 14; 2022: 11; 2023: 22; 2024: 11; 2025: 7; 2026: 12.

77 papers.

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  1. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 123
  2. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  3. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  4. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  5. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  6. 2021Distributionally Robust Learningcited by 44
  7. 2022Understanding and Mitigating Overfitting in Prompt Tuning for Vision-Language Modelscited by 40
  8. 2022Normalizing flow neural networks by JKO schemecited by 39
  9. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  10. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  11. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  12. 2023A mean-field games laboratory for generative modelingcited by 28
38 more
  1. 2024AWT: Transferring Vision-Language Models via Augmentation, Weighting, and Transportationcited by 27
  2. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  3. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  4. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  5. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  6. 2023Unifying GANs and Score-Based Diffusion as Generative Particle Modelscited by 21
  7. 2022Sliced Optimal Partial Transportcited by 19
  8. 2023Gaussian Interpolation Flowscited by 17
  9. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  10. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  11. 2021Stein Variational Gradient Descent: many-particle and long-time asymptoticscited by 15
  12. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  13. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  14. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
  15. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  16. 2023Properties of Discrete Sliced Wasserstein Lossescited by 12
  17. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  18. 2024Efficient Prior Calibration From Indirect Datacited by 11
  19. 2023Dynamic Flows on Curved Space Generated by Labeled Datacited by 10
  20. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  21. 2022Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimizationcited by 9
  22. 2024Neural Sinkhorn Gradient Flowcited by 8
  23. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  24. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  25. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  26. 2024Importance Corrected Neural JKO Samplingcited by 7
  27. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  28. 2021Learning to Generate Wasserstein Barycenterscited by 6
  29. 2023Measure transfer via stochastic slicing and matchingcited by 6
  30. 2023Scalable Counterfactual Distribution Estimation in Multivariate Causal Modelscited by 6
  31. 2024Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributionscited by 6
  32. 2026On the Wasserstein Gradient Flow Interpretation of Drifting Modelscited by 6
  33. 2023On the Convergence Rate of Gaussianization with Random Rotationscited by 5
  34. 2023One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Modelscited by 4
  35. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  36. 2023Module-wise Training of Neural Networks via the Minimizing Movement Schemecited by 4
  37. 2023Differentially Private Gradient Flow based on the Sliced Wasserstein Distancecited by 4
  38. 2024WeiPer: OOD Detection using Weight Perturbations of Class Projectionscited by 4

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