Sobolev Regularized MMD Gradient Flow

• URL: http://arxiv.org/abs/2605.11884v1
• Date: Tue, 12 May 2026 09:58:19 GMT
• Title: Sobolev Regularized MMD Gradient Flow
• Abstract summary: We propose a regularized variant of the gradient-regularized MMD flow.<n>The proposed regularization mitigates the difference between the mean kernel mean embeddings.<n>A key highlight of the proposed flow is that it is applicable in both sampling (from an unnormalized target distribution)
• Score: 22.929984194375805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates the non-convexity of the MMD objective and yields provable \emph{global} convergence guarantees in MMD in both continuous and discrete time. A more surprising appeal is that our convergence analysis does not rely on isoperimetric assumptions on the target distribution. Instead, it is based on a regularity condition on the difference between kernel mean embeddings. A key highlight of the proposed flow is that it is applicable in both sampling (from an unnormalized target distribution) -- using Stein kernels -- and generative modeling settings, unlike previous works, where a gradient flow is suitable for only generative modeling or sampling but not both. The effectiveness of the proposed flow is empirically verified on a broad range of tasks in both generative modelling and sampling.

Related papers

• Generative Modeling under Non-Monotonic MAR Missingness via Approximate Wasserstein Gradient Flows [6.221876252052772]
  We propose a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR)<n>FLOWGEM minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns.<n>It achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotonic MAR mechanisms.
  arXiv  Detail & Related papers  (2026-04-06T09:56:08Z)
• Fast Sampling for Flows and Diffusions with Lazy and Point Mass Stochastic Interpolants [5.492889521988414]
  We prove how to convert a sample path of a differential equation (SDE) with arbitrary diffusion coefficient under any schedule.<n>We then extend the interpolant framework to admit a larger class of point mass schedules.
  arXiv  Detail & Related papers  (2026-02-03T17:48:34Z)
• Gaussian Mixture Flow Matching Models [63.092956669059824]
  Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models re parameterize the Gaussian mean as flow velocity.<n>They underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG)<n>We introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality.
  arXiv  Detail & Related papers  (2025-04-07T17:59:42Z)
• Minimax Optimality of the Probability Flow ODE for Diffusion Models [8.15094483029656]
  This work develops the first end-to-end theoretical framework for deterministic ODE-based samplers.<n>We propose a smooth regularized score estimator that simultaneously controls both the $L2$ score error and the associated mean Jacobian error.<n>We demonstrate that the resulting sampler achieves the minimax rate in total variation distance, modulo logarithmic factors.
  arXiv  Detail & Related papers  (2025-03-12T17:51:29Z)
• Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts [64.34482582690927]
  We provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models.<n>We propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality.
  arXiv  Detail & Related papers  (2025-03-04T17:46:51Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• (De)-regularized Maximum Mean Discrepancy Gradient Flow [27.70783952195201]
  We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. DrMMD flow can simultaneously guarantee near-global convergence for a broad class of targets in both continuous and discrete time. Our numerical scheme uses an adaptive de-regularization schedule throughout the flow to optimally trade off between discretization errors and deviations from the $chi2$ regime.
  arXiv  Detail & Related papers  (2024-09-23T12:57:42Z)
• Sobolev Space Regularised Pre Density Models [51.558848491038916]
  We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive validation model clear and consistent.
  arXiv  Detail & Related papers  (2023-07-25T18:47:53Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows [10.406659081400354]
  Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one.
  arXiv  Detail & Related papers  (2020-06-28T10:39:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.