Diffusion from First Principles: From Data to Noise and Back
The one idea behind every diffusion model โ gradually destroy structure with noise, then learn to undo it โ with an interactive forward-diffusion explorable to build intuition.
๐ // 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.
// notes
The one idea behind every diffusion model โ gradually destroy structure with noise, then learn to undo it โ with an interactive forward-diffusion explorable to build intuition.
// coming soon
The discrete-time denoising objective from scratch โ the forward chain, the variational bound, why predicting ฮต works, and a minimal trainable implementation.
The continuous-time SDE view of diffusion โ score matching, the reverse-time SDE, and the deterministic probability-flow ODE that enables fast sampling.
Learning velocity fields directly โ conditional flow matching, straight-line probability paths, and how flow matching relates to (and simplifies) diffusion.