Machine learning, and more generally artificial intelligence (AI), is having a transformational impact on science, technology, and our daily lives. Approaches based on deep neural networks have achieved remarkable success in a variety of applications, such as the impressive performance on image, video, and text generation tasks when combined with diffusion models. Despite this, the present architectures lack reliability and performance guarantees. The goal of this project is to develop mathematically sound approaches to some of the relevant sampling tasks in high dimensions, which is typical in the AI setting and where classical computational approaches are unfeasible. The project is motivated by two tasks: one is the sampling of measures given by their density, which is the typical setting in many applications in physical sciences and Bayesian inference, and the other is creating new samples based on a family of examples, namely sampling in the generative setting. The goal is to create efficient approaches with rigorous performance guarantees. Graduate and undergraduate students will be involved in the research of this project, training a new generation of mathematicians who both have knowledge of modern techniques of applied analysis and are cognizant of important questions arising in data science and artificial intelligence. The project will investigate flow-based approaches to sampling that take the view of variational inference. In contrast to popular approaches to sa