The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer

The book is a compact, mathematically grounded introduction to how modern generative models work and how their ideas connect. Rather than cataloguing the latest architectures or implementation choices, it builds a guided path from familiar statistical tools toward major model families. The emphasis is on derivations and conceptual links, so readers can see not only what each method does but how its mathematical structure arises.

The progression includes principal component analysis and probabilistic PCA, then variational autoencoders and diffusion models, alongside normalising flows and autoregressive models. It also covers generative adversarial networks, Wasserstein GANs, and energy-based models. The aim is to make this range of approaches accessible without stripping away the mathematics needed to understand them. The revised 195-page version adds visual explanations throughout. It is intended for students, practitioners, and researchers who want a foundation for learning or working with generative AI, especially readers seeking an intuitive but derivation-oriented account rather than a broad survey of current systems.