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，标准化流通过微分同胚变换对基础分布进行变换，从而实现精确的似然估计。将标准化流框架扩展至处理时间索引流，便形成了动态标准化流——一种用于建模时间序列、随机过程和神经随机微分方程（SDEs）的强大工具。本文提出了一种新型动态标准化流变体——时间变换标准化流（TCNF），其基于布朗运动的时间变形构建，构成了一个通用且广泛的高斯过程族。该方法能够有效建模其他方法无法建模的某些随机微分方程，包括标准型如广为人知的Ornstein-Uhlenbeck过程，并推广了先前的方法，从而提升了结果质量与推理预测能力。