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.

翻译：本文提出一个通用框架，利用常微分方程和再生核希尔伯特空间实现概率测度的输运，以达成最小散度生成建模与采样，其灵感源自微分同胚匹配与图像配准思想。对所提方法进行了理论分析，给出了关于模型复杂度、训练集样本数量及模型设定误差的先验误差界。大量数值实验进一步揭示了该方法的性质、优势与局限，并将适用性扩展至条件模拟与推断等其他任务。