Diffusion models

The paper borrowed its method from statistical physics. Take an image and add a little Gaussian noise; repeat a thousand times and it becomes pure static, a process that is easy to describe and impossible to undo by inspection. But each small step of noising has a small step of denoising that is, in the limit, also Gaussian, and a neural network can be trained to predict it. Run the learned steps in reverse from static and you generate an image. Jascha Sohl-Dickstein's group at Stanford posted the idea on 12 March 2015 with results on small images and toy data.

It was overshadowed almost completely by generative adversarial networks, which produced sharper pictures and were the subject of a thousand papers over the next five years. Diffusion was slow, needing a thousand network evaluations per sample, and its samples were blurry.

Jonathan Ho, Ajay Jain and Pieter Abbeel's 2020 paper revived it with a simpler training objective and a better network, and showed it matching GANs on image quality; within two years it was DALL-E 2, Stable Diffusion and Midjourney, and the noise-to-image film that everyone has now seen. The 2015 paper is the source, and its physics framing, forward and reverse processes in and out of equilibrium, is still how the method is taught.