Semaine Mixte Sept 2026

Generative models

Sept 14-19, 2026

Outline

The goal of this course is to introduce the ideas of the most widely used generative models, the so-called score-based generative models. It will rely on a strong knowledge of probability theory and also some capacity to code in python, namely in PyTorch. All the practicals (and some more) are available at this repository. I highly encourage attending students to install all the recommended packages into a Python virtual environment. .

Prerequisites:

• Numerical Python (ie familiarity with programming in Python and the numpy, scipy, matplotlib librairies).
• Basics of Probability theory.
• Some knowledge in general machine learning and statistics is useful, but not strictly necessary.

Schedule

Monday, September 14, 2026

• The rules of the game: Exam, rattrapage, etc...
• What is generative modelling ?
• Probability recap.
• Distance between probability distributions and exercises .
• Practical: Evaluating distance between probability distributions .

Tuesday, September 15, 2026

• Markov chains, destroying information, recovering information and exercises
• Practical: Sampling from your first generative model
• Practical: Denoising images
• Learning the denoiser.
• Practical: Learning a denoiser in a toy setting

Wednesday, September 16, 2026

• Introduction to "minimal" stochastic processes
• Time reversal of "some" diffusion processes
• Theoretical exercises on diffusions

Thursday, September 17, 2026

• TBA

Friday, September 18, 2026

• 9:00 - 12:25 : Review of the course, Q&A and Exam preparation
• 14:00 - 17:00 : Exam

All course materials will be in English but some lectures might be given in French if all the audience speaks French.

Useful ressources

There is no single textbook for this course, but the following resources are relevant:

• Stochastic Calculus, Filtering, and Stochastic Control by Ramon Van Handel; I particularly like the refresher on probability theory as well as the introduction to Stochastic processes (Chapter 1).
• Markov Chains by Randal Douc, Eric Moulines, Pierre Priouret and Philippe Soulier; The reference for the theory of Markov chains, contains most of the results, although might be a bit hard to read for beginners.