Theoretical Foundations of Ethical and Interpretable Diffusion Models

Mentored by Guido Montúfar and Max von Renesse
at Max Planck Institute for Mathematics in the Sciences, Leipzig

Diffusion models are probability models that can generate high-quality data based on the data they are trained on. In spite of their success and quick adoption, these methods suffer from limitations, such as requiring large and diverse training data, lack of interpretability, and ethical concerns related to their potential of generating deceptive contents or violating intellectual property rights. This project aims at developing mathematical frameworks to improve the interpretability of generated data and control protected data in diffusion models. Methods include geometry of artificial neural networks, stochastic analysis, differential geometry, information theory, and optimal transport.

Work Environment

The Max Planck Institute for Mathematics in the Sciences is one of the leading research institutions in applied mathematics and interactions between mathematics and the sciences, with a lively guest program, dedicated staff and technical support, and excellent library and computing infrastructure. The candidate will work with the Math Machine Learning Group at MPI MiS and the Stochastic group at Leipzig University.

Prerequisites

Master’s degree in mathematics, statistics, computer science, or related areas. Demonstrated expertise in one or more of the following areas: deep learning, generative models, differential geometry, optimal transport, information theory, stochastic analysis.

Further details on the requirements and application process can be found in SECAI's announcement for open PhD positions in 2024.