Sobolev Regularized MMD Gradient Flow

ArXi:2605.11884v1 Announce Type: new We propose Sobole-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 surprising appeal is that our convergence analysis does not rely on isoperimetric assumptions on the target distribution.