The generative paradigm has become increasingly important in machine learning
and deep learning models. Among popular generative models are normalizing
flows, which enable exact likelihood estimation by transforming a base
distribution through diffeomorphic transformations. Extending the normalizing
flow framework to handle time-indexed flows gave dynamic normalizing flows, a
powerful tool to model time series, stochastic processes, and neural stochastic
differential equations (SDEs). In this work, we propose a novel variant of
dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on
time deformation of a Brownian motion which constitutes a versatile and
extensive family of Gaussian processes. This approach enables us to effectively
model some SDEs, that cannot be modeled otherwise, including standard ones such
as the well-known Ornstein-Uhlenbeck process, and generalizes prior
methodologies, leading to improved results and better inference and prediction
capability.

本论文介绍了一种新变种的动态归一化流模型（TCNF），基于布朗运动的时间变形，能够有效地建模一些随机微分方程，包括标准的奥恩斯坦 - 乌伦贝克过程，并且提供更好的推断和预测能力。