Diffeomorphic Measure Matching with Kernels for Generative Modeling

2024/02/12 by Biraj Pandey, Pandey, Biraj, Bamdad Hosseini +5 · 1 citation
Mathematics · #35Q68 49Q22 62F15 68T07 62R07 #Computation (stat.CO) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2402.08077

openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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