mlsanityData to 7 Oct 2026

Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel

arXiv 2310.03054 ↗First posted 4 Oct 2023stat.ML cs.LG math.OCcited by 25

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Abstract (arXiv)

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 41 of its 74 references that are in the map. First posted on arXiv 4 Oct 2023.

Builds on

41 of 74 references.

References · 41

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29 more
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  3. 2019Generalized Sliced Wasserstein Distancescited by 205
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  12. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  13. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  14. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  15. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 11; 2025: 7; 2026: 5.

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  1. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  2. 2024Deep MMD Gradient Flow without adversarial trainingcited by 18
  3. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  4. 2024Fast Kernel Summation in High Dimensions via Slicing and Fourier Transformscited by 7
  5. 2024Importance Corrected Neural JKO Samplingcited by 7
  6. 2024Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functionscited by 7
  7. 2024Fast Summation of Radial Kernels via QMC Slicingcited by 7
  8. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  9. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  10. 2025DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flowscited by 4
  11. 2023Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distancescited by 3
  12. 2024Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flowcited by 3
13 more
  1. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  2. 2025Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flowscited by 2
  3. 2026Three-Body Scattering for Generative Modelingcited by 2
  4. 2024Mixed Noise and Posterior Estimation with Conditional DeepGEMcited by 1
  5. 2024Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximizationcited by 0
  6. 2024Conditional Generative Models for Contrast-Enhanced Synthesis of T1w and T1 Maps in Brain MRIcited by 0
  7. 2025Contextual Scenario Generation for Two-Stage Stochastic Programmingcited by 0
  8. 2025Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifoldcited by 0
  9. 2025A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Modelscited by 0
  10. 2025One-shot Conditional Sampling: MMD meets Nearest Neighborscited by 0
  11. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  12. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0
  13. 2026Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energiescited by 0