Diffusion Models, Sampling and Stochastic Localization
Spring 2024
 Lecturer
 Yuansi Chen
 Lecture Time
 Tue 10:1512:00 (from 16.04.2024 to 28.05.2024), HG G 26.5
 Course Number
 401463424L/4014634DRL
 Office Hours
 Tue 3:004:00 (from 16.04.2024 to 28.05.2024), HG G 15.1
Content
Selected topics on Markov chain Monte Carlo sampling algorithms, diffusion generative models and related proof techniques.
The official course catalogue page can be found
here.
Prerequisites
We assume basic knowledge of linear algebra, introduction to probability and statistics.
Familarity with convex optimization, stochastic process and stochastic calculus would help.
Lecture notes
(tentative, please refresh page)
Date 
Content 
Notes 
Tu 16.04.

Introduction  two settings of sampling

Lecture 1

Tu 23.04.

Geometric randon walks  ball walk and hitandrun

Lecture 2

Tu 30.04.

Langevin diffusion and Langevin algorithms

Lecture 3

Tu 07.05.

Rest of ULA and intro to Diffusion models

Lecture 4

Tu 14.05.

Diffusion model and its convergence

Lecture 5

Tu 21.05.

Rest of diffusion model convergence and simulation

Lecture 6

Tu 28.05.

Stochastic localization and its relation to diffusion models

Lecture 7

Suggested readings
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Extended readings and project ideas
A few vague ideas:

Diffusion models for sampling models in statistical physics

Diffusion type models for parallel sampling of discrete distributions
 New ideas in sampling multimodal distributions

Stochastic localization related

Proximal sampling and related

Better analysis for higher order sampling algorithms
Literature
Acknowledgement
This course contains materials such as lecture notes/slides that were developed or adapted from many other courses. Especially,