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.

翻译：生成范式在机器学习和深度学习模型中日益重要。在流行的生成模型中，归一化流通过微分同胚变换基础分布实现精确似然估计。将归一化流框架扩展至处理时间索引流，形成了动态归一化流——这是一种能够建模时间序列、随机过程和神经随机微分方程（SDE）的强大工具。本文提出了一种新型动态归一化流变体——时间变换归一化流（TCNF），其基于布朗运动的时间形变，构成了一个通用且广泛的高斯过程族。该方法使我们能够有效建模其他方法无法建模的某些SDE（包括经典的奥恩斯坦-乌伦贝克过程等标准模型），并泛化了先前方法，从而获得更优结果与更强的推断及预测能力。