Scoring matching (SM), and its related counterpart, Stein discrepancy (SD) have achieved great success in model training and evaluations. However, recent research shows their limitations when dealing with certain types of distributions. One possible fix is incorporating the original score matching (or Stein discrepancy) with a diffusion matrix, which is called diffusion score matching (DSM) (or diffusion Stein discrepancy (DSD)). However, the lack of interpretation of the diffusion limits its usage within simple distributions and manually chosen matrix. In this work, we plan to fill this gap by interpreting the diffusion matrix using normalizing flows. Specifically, we theoretically prove that DSM (or DSD) is equivalent to the original score matching (or Stein discrepancy) evaluated in the transformed space defined by the normalizing flow, where the diffusion matrix is the inverse of the flow's Jacobian matrix. In addition, we also build its connection to Riemannian manifolds and further extend it to continuous flows, where the change of DSM is characterized by an ODE.

本文利用正则化流对扩散匹配进行建模，使扩散匹配等同于转换空间中的原始得分匹配，扩散矩阵是流雅可比矩阵的倒数，建立其与黎曼流形的联系，并将其扩展到连续流中。

使用归一化流理解扩散得分匹配