Diffusion model
Also: denoising diffusion model, DDPM
A fixed forward process adds Gaussian noise to data over T steps; a neural network (often a U-Net or Transformer) is trained to predict the added noise at each step. Sampling starts from random noise and repeatedly subtracts the predicted noise, which is stable to train but needs many steps.
xₜ = √ᾱₜ · x₀ + √(1 − ᾱₜ) · ε, ε ~ N(0, I)
Example
At a step where ᾱₜ = 0.25, the noisy sample is xₜ = 0.5·x₀ + 0.866·ε; the network sees xₜ and t and is trained to output ε. Generation then runs about T = 1,000 such steps in reverse.