Diffusion Models, Sampling and Stochastic Localization
Spring 2024
- Lecturer
- Yuansi Chen
- Lecture Time
- Tue 10:15-12:00 (from 16.04.2024 to 28.05.2024), HG G 26.5
- Course Number
- 401-4634-24L/401-4634-DRL
- Office Hours
- Tue 3:00-4:00 (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 hit-and-run
|
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,