five families of generative models
split by what they model and how they sample
p_data(x)
unknown, want sampler
1. explicit, tractable
p(x) = ∏ p(x_i | x_<i)
autoregressive: GPT, PixelCNN
flows: Glow, RealNVP
exact log p(x)
slow sequential inference
architecture restrictions (flows)
2. explicit, approximate
maximize ELBO ≤ log p(x)
VAE: encoder + decoder
diffusion: DDPM, SD3
dominant in 2026
iterative sampling (20-50 steps)
scales to text, image, video, 3D
3. implicit density
G(z) -> x, D(x) -> real/fake
GAN, StyleGAN, Pix2Pix
one-shot sampling
no log p(x) at all
training instability, mode collapse
still SOTA for narrow photoreal
4. score / continuous-time
learn s(x) = ∇_x log p(x)
score SDE, flow matching
rectified flow, consistency models
simulation-free training
straight paths => 1-4 step sampling
5. tokens + AR transformer
VQ-VAE + transformer over tokens
DALL-E 1, Parti, MuseNet
AudioLM, VALL-E, MusicGen, Sora patches
reuse LLM stack
quality bounded by tokenizer