[Submitted on 28 May 2026 (v1), final revised 8 Sep 2026 (this version, v2)]
Abstract:This publish provides a compact, derivation-oriented introduction to the mathematical foundations of contemporary generative synthetic intelligence. Rather than surveying all latest architecture or implementation detail, it develops a coherent path through the ideas connecting important families of generative models, from PCA, probabilistic PCA, variational autoencoders, and diffusion models to normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. The aim is to create the construction of generative modelling additional accessible without removing the mathematical matter needed to comprehend how these models are derived and related. The publish is intended as a foundation-building primer for mathematically inquisitive researchers, practitioners, and students.
Submission history
From: Tianhua Chen [view email]
[v1] Thu, 28 May 2026 10:12:00 UTC (125 KB)
[v2] Tue, 8 Sep 2026 07:17:36 UTC (1,168 KB)
.png)
