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:

1Measure Theory for Probability, Ito Integrals, Martingales
2Forward (FPK) and Backward Kolmogorov Equations, Infinitesimal Generator
3Ito’s Lemma
4Linear SDEs and the OU process
5Time reversal
6Doob’s h-transform and conditioning SDEs
7Probability flow ODE and flow matching
8Girsanov’s Theorem, KL divergence in path space
9Half Bridges and Stochastic Control
10Schroedinger Bridges

These topics will be covered in 4 sessions, with the first two being 90 minutes and the last two being 60 minutes.