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.

该文章提出了一个概率测度传输的一般框架，利用常微分方程和再生核希尔伯特空间进行最小差异生成建模和采样，受到微分同胚匹配和图像注册的思想的启发。通过理论分析，给出了该方法的先验误差界限，包括模型复杂度、训练集中的样本数量和模型规范错误等因素。大量的数值实验进一步展示了该方法的特性、优势和弱点，并扩展了其在条件模拟和推理等其他任务中的适用性。