Diffeomorphic Measure Matching with Kernels for Generative Modeling

Both the paper and the candidate solution prove the same three-term high-probability bound for the MMD of the learned flow: (i) a discretization term scaling like (exp(C1 r)−1) h_S^k, (ii) a statistical term of order N^{-1/2}, and (iii) an approximation/model-misspecification term involving inf_{v∈QQQ_r} ||v−v†||_∞ with a Grönwall factor. The technical ingredients and structure are essentially identical: stability of ODE flows (Grönwall), Lipschitz stability of MMD under perturbations of the transport map, kernel interpolation on scattered sets, and a generalization bound for minimum-MMD learning. The only material difference is the justification of the statistical term: the paper invokes a dedicated generalization theorem for minimum-MMD estimators, while the model sketches a uniform Rademacher argument; the conclusion matches but the paper’s route is cleaner and avoids subtle measurability/dependence issues.