Interactive Notes

Tangents, cotangents, and what composes: jvp and vjp as exact pushforward and pullback on real and complex space, worked out down to an exterior derivative in a few lines of JAX.

Generative models, from change of variables, continuous flows, and the fixed-path trick behind diffusion models to flow matching, physics applications, and few-step distillation.

Smooth, closed-form-invertible scalar bijections on the whole real line: building blocks for normalizing flows that keep smoothness, an unbounded domain, a cheap exact inverse, and local expressivity all at once.