About
SDEs and Diffusion Models - Kieran Didi and Francisco Vargas, R255 module Cambridge University, Lent 2024
Hey everyone! This is a course about the theory of SDEs and how it can be applied to diffusion models. We will introduce the foundations of Ito Calculus and apply them to diffusion processes within generative modelling, sampling and data assimilation.
The modules in this course are the following:
| Topic | Content |
|---|---|
| 1 | Measure Theory for Probability, Ito Integrals, Martingales |
| 2 | Forward (FPK) and Backward Kolmogorov Equations, Infinitesimal Generator |
| 3 | Ito’s Lemma |
| 4 | Linear SDEs and the OU process |
| 5 | Time reversal |
| 6 | Doob’s h-transform and conditioning SDEs |
| 7 | Probability flow ODE and flow matching |
| 8 | Girsanov’s Theorem, KL divergence in path space |
| 9 | Half Bridges and Stochastic Control |
| 10 | Schroedinger Bridges |
These topics will be covered in 4 sessions, with the first two being 90 minutes and the last two being 60 minutes.