Diffeomorphic Measure Matching with Kernels for Generative Modeling
Biraj Pandey Bamdad Hosseini Pau Batlle Houman Owhadi
This article presents a general framework for the transport of probability
measures towards minimum divergence generative modeling and sampling using
ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces
(RKHSs), inspired by ideas from diffeomorphic matching and image registration.
A theoretical analysis of the proposed method is presented, giving a priori
error bounds in terms of the complexity of the model, the number of samples in
the training set, and model misspecification. An extensive suite of numerical
experiments further highlights the properties, strengths, and weaknesses of the
method and extends its applicability to other tasks, such as conditional
simulation and inference.