mlsanityData to 7 Oct 2026

Generative Sliced MMD Flows with Riesz Kernels

arXiv 2305.11463 ↗First posted 19 May 2023cs.LG math.PR stat.MLcited by 36

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Abstract (arXiv)

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|r, r ∈ (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(√d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 52 of its 90 references that are in the map. First posted on arXiv 19 May 2023.

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52 of 90 references.

References · 52

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Citing papers per year: 2023: 1; 2024: 11; 2025: 14; 2026: 10.

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  1. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  2. 2024Deep MMD Gradient Flow without adversarial trainingcited by 18
  3. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  4. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  5. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 10
  6. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  7. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  8. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  9. 2024Fast Kernel Summation in High Dimensions via Slicing and Fourier Transformscited by 7
  10. 2024Interaction-Force Transport Gradient Flowscited by 7
  11. 2024Importance Corrected Neural JKO Samplingcited by 7
  12. 2024Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functionscited by 7
24 more
  1. 2024Fast Summation of Radial Kernels via QMC Slicingcited by 7
  2. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  3. 2024Paired Wasserstein Autoencoders for Conditional Samplingcited by 5
  4. 2025DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flowscited by 4
  5. 2025Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regimecited by 4
  6. 2024Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergencecited by 3
  7. 2025Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysiscited by 3
  8. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  9. 2025Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flowscited by 2
  10. 2025Stationary MMD Pointscited by 2
  11. 2025Sequence Modeling with Spectral Mean Flowscited by 2
  12. 2025Sliced ReLU attention: Quasi-linear contextual expressivity via sortingcited by 2
  13. 2026Three-Body Scattering for Generative Modelingcited by 2
  14. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  15. 2026A Kernel Approach for Semi-implicit Variational Inferencecited by 1
  16. 2025Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operatorscited by 0
  17. 2025One-shot Conditional Sampling: MMD meets Nearest Neighborscited by 0
  18. 2026Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspectivecited by 0
  19. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0
  20. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0
  21. 2026Fast Gauss Sums via Flash Attentioncited by 0
  22. 2026Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energiescited by 0
  23. 2026One-Step Generative Modeling via Unbalanced Optimal Transportcited by 0
  24. 2026Quasi Linear Kernel Attention with Infinite Capacitycited by 0