Course Notes

The course notes serve as the backbone of the course and provide a self-contained explanation of all material in the class. We strongly recommend using them. You can view the notes by clicking the button below:

To cite these lecture notes, please use:

@misc{flowsanddiffusions2026,
  author       = {Peter Holderrieth and Ezra Erives},
  title        = {Introduction to Flow Matching and Diffusion Models},
  year         = {2026},
  url          = {https://diffusion.csail.mit.edu/},
  eprint       = {2506.02070},
  archivePrefix = {arXiv}
}
  

Lectures

Lecture	Topic	Slides	Recording
1	Flow and Diffusion Models Introduction to generative models Ordinary and stochastic differential equations Sampling from flow and diffusion models	[slides 1]
2	Flow Matching Conditional and marginal probability path Conditional and marginal vector field Flow matching training objective	[slides 2]
3-A	Score Functions and Score Matching Score functions Denoising score matching SDE sampling	[slides 3]
3-B	Classifier-free Guidance Guided generation Classifier guidance Classifier-free guidance	[slides 3]
4	Latent Spaces and Neural Network Architectures Variational autoencoders and latent spaces Diffusion Transformer and U-Nets Case studies: Large-scale models	[slides 4]
5	Discrete Diffusion Models Continuous-time Markov chains (CTMCs) Sampling from CTMC models Training CTMC models	[slides 5]

Labs

There are 3 labs given as exercises accompanying the class to give you hands-on practical experience. The labs will guide you through building a flow matching and diffusion model from scratch step-by-step. To do the exercises, perform the following steps:

1. Click on the lab link below to view the lab instructions.
2. Download the .ipynb notebook from GitHub and open it in your favorite Jupyter notebook environment (one good choice is Google Colab).
3. Follow the instructions in the lab to complete the exercises.
4. Once all questions have been completed, export your notebook to a PDF and submit to Gradescope via Canvas. Please do not clear cell output, as this makes it harder to grade!

Stuck? Solutions can be found here.

Instructors

Prerequisites: Linear algebra, multivariate calculus, and basic probability theory. Students should be familiar with Python and have some experience with PyTorch.

Acknowledgements

We would like to thank:

• Professor Tommi Jaakkola for advising and sponsoring this class
• Ashay Athalye (Students for Open and Universal Learning) for excellent video editing.
• Lisa Bella, Ellen Reid, and the team at MIT EECS
• Christian Fiedler, Tim Griesbach, Benedikt Geiger, and Albrecht Holderrieth
• Elaine Mello (MIT Open Learning)
• Cameron Diao, Tally Portnoi, Andi Qu, Roger Trullo, Ádám Burián, Zewen Yang, and many others
• The Missing Semester
• Participants in MIT 6.S184 (IAP 2026)

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