Tianhua Chen’s 195-page primer connects generative models through their mathematics. It starts with PCA, a way to compress data along its strongest directions, and introduces probability and calculus as they become necessary.

  • From compression to generation: probabilistic PCA adds hidden variables and noise. Variational autoencoders extend that idea with neural networks and a learnable approximation to otherwise difficult probability calculations.
  • Two views of diffusion: a sequence of noisy hidden states connects to a learned field of denoising directions. The book explains how those directions can guide noise back toward data.
  • Different ways to learn distributions: invertible transformations and ordered predictions keep likelihood calculations exact. Adversarial models compare samples; energy-based models learn landscapes of relative plausibility.

September’s v2 adds visual explanations and clarifies an important detail: the exact diffusion training bound gives different weights to different noise levels. The common simplified noise-prediction loss drops those weights.

Caveat: this is a working mathematical primer, not a new experimental result. Its language-model coverage explains ordered prediction rather than teaching transformer architecture or coding-agent practice.

What the discussion adds

The 42-comment thread on Hacker News adds alternatives for readers choosing a study path.

What the thread adds

  • Valk3_ — answering nblgbg’s request for exercises, recommends Simon Prince’s Understanding Deep Learning: “Has both theoretical and programming exercises.”
  • hasteg — recommends Anil Ananthaswamy’s Why Machines Learn as a gentler introduction for readers with less mathematical background.
  • StilesCrisis — objects to unexplained basis-vector notation. apricot replies that the vectors are explicitly defined; mkl says the unit-vector hat could still use explanation. Readers disagree about the assumed starting knowledge.

HN handles are pseudonymous, and HN publishes no per-comment scores. The fetched order is HN’s ranking; this is a slice of the thread, not a consensus.