  Denoising diffusion probabilistic models (DDPM) are a class of generative
models which have recently been shown to produce excellent samples. We show
that with a few simple modifications, DDPMs can also achieve competitive
log-likelihoods while maintaining high sample quality. Additionally, we find
that learning variances of the reverse diffusion process allows sampling with
an order of magnitude fewer forward passes with a negligible difference in
sample quality, which is important for the practical deployment of these
models. We additionally use precision and recall to compare how well DDPMs and
GANs cover the target distribution. Finally, we show that the sample quality
and likelihood of these models scale smoothly with model capacity and training
compute, making them easily scalable. We release our code at
https://github.com/openai/improved-diffusion
