Resources

Here you will find resources relevant to the course, first some general ones and after that additional resources to some of the specific topics we discuss in the course.

Books

• Oksendal - Stochastic Differential Equations, formal treatment and introduction to the Ito Integral
• Särkkä & Solin - Applied Stochastic Differential Equations, quick usage / intuition of the SDE theorems and properties
• Pavliotis - Stochastic Processes and Applications, physicsy / functional analysis type of introduction
• Von Kampen - Stochastic Processes in Physics and Chemistry, physics/chemistry focused introduction

Publications

• Denoising Diffusion Probabilistic Models
• Score-Based Generative Modeling through Stochastic Differential Equations
• Simulating Diffusion Bridges with Score Matching
• First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Data
• Denoising Diffusion Samplers
• Solving Schrödinger Bridges via Maximum Likelihood

Practicals/Notebooks

• Prince - Understanding Deep Learning Textbook, notebooks for diffusion chapter
• CVPR 2022 Tutorial - Denoising Diffusion-based Generative Modeling: Foundations and Applications
• Yang Song SDE paper codebase, includes pedagogical notebook

Websites

• Applied SDE Course by Särkkä & Solin

Measure Theory Resources

• Lecture on measure and integration, Cambridge-only access
• Notebook with DCT example
• YouTube Playlist with Measure Theory Concepts

Convergence of the OU process - Additional Resources

For this we use the mostly Pavliotis book[2]

1. OU process Intro: Section 4.2 Pavliotis
2. OU process and Hermite Polynomials: Section 4.4 Pavliotis
3. OU process Mixing: Chapter 2.7.1 and 2.7.2 Bakry book[1]
4. Over-dampened Langevin dynamics (equilibrium methods): Section 4.5 Pavliotis

[1] D. Bakry, I. Gentil, and M. Ledoux. Analysis and geometry of Markov diffusion operators. Vol. 348. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Cham, 2014, pp. xx+552 [2] Pavliotis, G.A., 2014. Stochastic processes and applications: diffusion processes, the Fokker-Planck and Langevin equations (Vol. 60). Springer.