Mathematics of diffusion models
November 6-7th, 2025

Abstract
We will focus on score-based generative models, which rely on diffusion equations. If necessary, we will begin with a brief review of stochastic calculus in order to properly introduce and handle the mathematical objects involved. Once the models are presented, we will discuss the typical generalization bounds obtained, before turning to more recent developments that aim to shed light on favorable mechanisms arising during score learning. In particular, we will examine the phenomenon of memorization and how it can be mitigated by using sufficiently large steps in the SGD strategy employed to learn the score. Finally, we will highlight the connection between the diffusion stopping time and the underlying structure of the data.

Abstract
Diffusion models are a powerful framework for generative modeling, with applications ranging from image, audio or tabular data synthesis to LLM, reinforcement learning and beyond. But moving from elegant theory to practical implementation raises some key questions: how do you build, load and customise a model that truly fits your problem? How can you generate highly specific data? How can you detect and evaluate biases in existing models? In this seminar, we’ll explore practical guidelines for selecting and implementing diffusion models, balancing trade-offs such as computation time, cost, trustworthiness and task efficiency. We’ll also dive into bias in generative AI, showing how revealing and measuring bias can be a challenging task, especially for large language models (LLMs). A hands-on case study will illustrate the strengths and limitations of the diffusion-model approach, sparking discussion on what it really takes to bring diffusion models from theory to real-world applications. A practical session will be conducted in Python.