The forward and reverse processes of a diffusion model

Explain how a diffusion model is trained and how it generates. Describe the forward process that adds noise step by step, the reverse process the network learns, the usual training target (predicting the added noise) and why it is a simple regression loss. Then contrast training, where a random step is sampled per example, with generation, which walks all the steps back from pure noise, and say how samplers cut the number of steps.