mlsanityData to 7 Oct 2026

Sliced Wasserstein with Random-Path Projecting Directions

arXiv 2401.15889 ↗First posted 29 Jan 2024stat.ML cs.AI cs.CVcited by 15

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Abstract (arXiv)

Slicing distribution selection has been used as an effective technique to improve the performance of parameter estimators based on minimizing sliced Wasserstein distance in applications. Previous works either utilize expensive optimization to select the slicing distribution or use slicing distributions that require expensive sampling methods. In this work, we propose an optimization-free slicing distribution that provides a fast sampling for the Monte Carlo estimation of expectation. In particular, we introduce the random-path projecting direction (RPD) which is constructed by leveraging the normalized difference between two random vectors following the two input measures. From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i.e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW). We then discuss the topological, statistical, and computational properties of RPSW and IWRPSW. Finally, we showcase the favorable performance of RPSW and IWRPSW in gradient flow and the training of denoising diffusion generative models on images.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 36 of its 53 references that are in the map. First posted on arXiv 29 Jan 2024.

Builds on

36 of 53 references.

References · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2018Computational Optimal Transportcited by 765
  6. 2021Score-based Generative Modeling in Latent Spacecited by 634
  7. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 515
  8. 2019Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptationcited by 235
  9. 2018Partial Adversarial Domain Adaptationcited by 127
  10. 2018Improving GANs Using Optimal Transportcited by 122
  11. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
  12. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
24 more
  1. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  2. 2020Distributional Sliced-Wasserstein and Applications to Generative Modelingcited by 69
  3. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  4. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  5. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  6. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  7. 2022Spherical Sliced-Wassersteincited by 31
  8. 2020The Power Spherical distributioncited by 27
  9. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  10. 2019Approximate Bayesian Computation with the Sliced-Wasserstein Distancecited by 22
  11. 2023Quasi-Monte Carlo for 3D Sliced Wassersteincited by 22
  12. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  13. 2022Sliced Optimal Partial Transportcited by 19
  14. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
  15. 2022Sliced Wasserstein Variational Inferencecited by 17
  16. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  17. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  18. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  19. 2023Slicing Unbalanced Optimal Transportcited by 10
  20. 2023Lidar Upsampling with Sliced Wasserstein Distancecited by 8
  21. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  22. 2023Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstructioncited by 7
  23. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  24. 2023Partial Transport for Point-Cloud Registrationcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 8; 2026: 2.

15 papers.

Sort:

  1. 2024Revisiting Deep Audio-Text Retrieval Through the Lens of Transportationcited by 10
  2. 2025Color Conditional Generation with Sliced Wasserstein Guidancecited by 10
  3. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  4. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  5. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  6. 2025Efficient Transferable Optimal Transport via Min-Sliced Transport Planscited by 4
  7. 2025Tree-Sliced Wasserstein Distance with Nonlinear Projectioncited by 3
  8. 2024Understanding Learning with Sliced-Wasserstein Requires Rethinking Informative Slicescited by 2
  9. 2024SAVA: Scalable Learning-Agnostic Data Valuationcited by 1
  10. 2025An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graphcited by 0
  11. 2025Relation-Aware Slicing in Cross-Domain Alignmentcited by 0
  12. 2025Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimizationcited by 0
3 more
  1. 2025ReSWD: ReSTIR'd, not shaken. Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reductioncited by 0
  2. 2026Convergence of empirical subgradients for optimal transport-based objectivescited by 0
  3. 2026Field Codes for Distributed Coupling Samplers and Certified Empirical Transportcited by 0

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  1. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  2. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
  3. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  4. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process
  5. 2023Learn to Optimize Denoising Scores for 3D Generation: A Unified and Improved Diffusion Prior on NeRF and 3D Gaussian Splatting
  6. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients
  7. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplers
  8. 2026Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance