Neural Stochastic Differential Equations for Probabilistic Modeling - Machine Learning, Sampling, and Inference

Stochastic differential equations (SDEs) offer a natural framework for probabilistic modeling of high-dimensional data, and underlie much progress in generative AI. This book presents a scalable framework for SDEs in machine learning, developed by the authors: training neural networks to approximate stochastic processes, and performing tractable inference and sampling via efficient SDE solvers. We introduce approaches to learning SDEs for probabilistic modeling, including fitting non-linear SDEs with neural networks, and a novel model that learns SDE dynamics under given constraints on its marginal probability. We also develop an efficient algorithm for sampling from high-dimensional SDEs, effective for generating diverse, high-fidelity images and videos. Written for researchers and students in computer science, engineering, and mathematics, this book offers a principled, unified treatment of the mathematical foundations behind techniques now standard in generative modeling.