Generative AI: Diffusion & Flow Models from First Principles

โ† All research notes

๐ŸŒ€ // generative ai series ยท 1 note

A build-from-scratch journey through modern generative modeling โ€” diffusion models, score matching, and flow matching โ€” derived from first principles, implemented in code, and made interactive so you can build intuition by playing with the math. This series doubles as the backbone of a lecture I'm giving in Fall 2026.

Coming soon Expected Fall 2026

Denoising Diffusion Probabilistic Models (DDPM), Step by Step

The discrete-time denoising objective from scratch โ€” the forward chain, the variational bound, why predicting ฮต works, and a minimal trainable implementation.

generative-aidiffusionddpmtraining
Coming soon Expected Fall 2026

Score-Based Models & the Probability-Flow ODE

The continuous-time SDE view of diffusion โ€” score matching, the reverse-time SDE, and the deterministic probability-flow ODE that enables fast sampling.

generative-aiscore-matchingsdesampling
Coming soon Expected Fall 2026

Flow Matching & Continuous Normalizing Flows

Learning velocity fields directly โ€” conditional flow matching, straight-line probability paths, and how flow matching relates to (and simplifies) diffusion.

generative-aiflow-matchingcnfoptimal-transport