14.2 A taxonomy
Six families currently dominate the landscape, and we shall meet each in turn. The taxonomy below frames them in a single picture.
| Family | Density | Training signal | Sampling | Notable |
|---|---|---|---|---|
| Autoregressive | Tractable, exact | Cross-entropy | Sequential, slow | GPT, PixelCNN |
| Latent-variable (VAE) | Variational lower bound | ELBO | One forward pass | VAE, β-VAE, VQ-VAE |
| Normalising flows | Tractable, exact | Log-likelihood | One forward pass | RealNVP, Glow |
| Energy-based | Unnormalised | Score matching, contrastive divergence | MCMC / Langevin | Hopfield, RBM |
| GAN | Implicit | Adversarial | One forward pass | DCGAN, StyleGAN |
| Diffusion | Score / noise-prediction | Denoising MSE | Many denoising steps | DDPM, Stable Diffusion |
The remainder of this chapter takes each family in turn, derives the central mathematics, and gives a worked PyTorch implementation where appropriate. We close with a from-scratch DDPM in §14.16.