tl;dr: A 195-page derivation-focused primer on the mathematics behind modern generative models, tracing a coherent path from PCA and probabilistic PCA through VAEs, diffusion models, normalizing flows, autoregressive models, GANs, Wasserstein GANs, and energy-based models. Rather than cataloging architectures or implementation details, it emphasizes how these model families are derived and connected, aimed at mathematically inclined researchers, students, and practitioners.