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

This revised 195-page preprint offers a compact, derivation-oriented introduction to the mathematical foundations of generative AI, tracing a coherent path from PCA and probabilistic PCA through variational autoencoders, diffusion models, normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. It aims to make the structure of generative modelling more accessible while retaining the mathematics needed to understand how these models are derived and related, and is intended for mathematically curious researchers, practitioners, and students. The version adds visual explanations throughout and welcomes comments and corrections.