Ho, Jain, Abbeel (2020) gave the field a recipe it could not quit. Destroy the data with noise over a thousand small steps. Train one neural net to predict the noise. Reverse the process at inference. Today every mainstream image, video, 3D, and music model runs on this loop, possibly with flow matching or consistency tricks on top.
You want a sampler for p_data(x). GANs play a minimax game that often diverges. VAEs produce blurry samples from a Gaussian decoder. What you really want is a training objective that is (a) a single stable loss (no saddle point, no minimax), (b) a lower bound on log p(x) (so you have likelihoods), and (c) samples that match SOTA quality.
Sohl-Dickstein et al. (2015) had a theoretical answer: define a Markov chain q(x_t | x_{t-1}) that gradually adds Gaussian noise, and train a reverse chain p_θ(x_{t-1} | x_t) to denoise. Ho, Jain, Abbeel (2020) showed the loss could be simplified to one line — predict the noise — and cleaned up the math. In 2020 this was a curiosity. In 2021 it produced state-of-the-art samples. In 2022 it became Stable Diffusion. In 2026 it is the substrate.
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