Lecturer

Yuansi Chen

Lecture Time

Mon 14:00-16:00 (from 16.02.2026 to 18.05.2026), HG E 21

Teaching Assistant

Tristan Matsulevits (tmatsulev at student.ethz.ch)

Course Number

401-4634-24L

Office Hours

Mon 16:00-17:00 (from 16.02.2026 to 18.05.2026), HG G 15.1 (Yuansi)

Tue 15:00-16:00 (from 16.02.2026 to 18.05.2026), NO E 39 (Tristan)

Content

Selected topics on diffusion generative models, Markov chain sampling 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, statistical learning theory, stochastic process and stochastic calculus would help.

Lecture notes

(keeps updating, check back later for more lectures)
For background on stochastic differential equations, see SDE bootcamp sheet

Suggested readings

Lecture 1

• Introduction of Sampling, Diffusions, and Stochastic Localization , Montanari 2023
• Nonparametric density estimation course notes from Computational Statistics

Lecture 2-3

• Chapter 1 on Langevin Diffusion in Continuous Time in Log-Concave sampling, Chewi 2024
• Estimation of Non-Normalized Statistical Models by Score Matching, Hyvarinen 2005
• Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices, Vempala and Wibisono 2022

Lecture 4-5

• Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , Geman and Geman, 1984
• Time reversal of diffusions., Haussmann and Pardoux, 1985/1986
• An entropy approach to the time reversal of diffusion processes, Föllmer, 1985
• Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions, Chen et al. 2022

Lecture 6-7

• Nearly d-linear convergence bounds for diffusion models via stochastic localization, Benton, De Bortoli, Doucet and Deligiannidis, 2023
• An entropy approach to the time reversal of diffusion processes, Föllmer, 1985

Lecture 8

• From optimal score matching to optimal sampling, Dou, Kotekal, Xu, and Zhou, 2023
• Optimal score estimation via empirical Bayes smoothing, Wibisono, Wu and Yang, 2024
• Learning general Gaussian mixtures with efficient score matching, Chen, Kontonis and Shah, 2024

Lecture 9

• Neural ordinary differential equations, Chen, Rubanova, Bettencourt, and Duvenaud 2018
• Denoising diffusion implicit models, Song, Meng and Ermon 2020
• Flow matching for generative modeling, Lipman, Chen, Ben-Hamu, Nickel and Le 2022
• Flow straight and fast: Learning to generate and transfer data with rectified flow, Liu, Gong and Liu 2022

Lecture 10

• Classifier-Free Diffusion Guidance, Ho and Salimans 2022
• DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models, Ren, Gao, Ying, Rotskoff and Han 2025

Lecture 11

• Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models, Li and Yan 2024
• Linear Convergence of Diffusion Models Under the Manifold Hypothesis, Potaptchik, Azangulov and Deligiannidis 2024

Coding exercises

Checkout the Github repo https://github.com/yuachen/course_diffusion_models

Literature

• The Principles of Diffusion Models, from Origins to Advances, Lai, Song, Kim, Mitsufuji and Ermon, 2025
• Continuous martingales and Brownian motion, Revuz and Yor, 2005
• Stochastic Differential Equations : An Introduction with Applications, Øksendal 2003
• Partial Differential Equations, Jost 2007, mainly Chapter 7 The Heat Equation, Semigroups, and Brownian Motion
• Log-Concave sampling, Chewi 2024

Acknowledgement

This course contains materials such as lecture notes/slides that were developed or adapted from many other courses. Especially,

• Introduction to Flow Matching and Diffusion Models 2026 , offered at MIT
• Convergence of Markov Chains, by Ravi Montenegro
• Continuous Algorithms, by Kevin Tian