Denoising Diffusion Generative Models in Graph ML

The breakthrough in Denoising Diffusion Probabilistic Models (DDPM) happened about 2 years ago. Since then, we observe dramatic improvements in generation tasks: GLIDE, DALL-E 2, Imagen, Stable Diffusion for images, Diffusion-LM in language modeling, diffusion for video sequences, and even diffusion for reinforcement learning. Diffusion might be the biggest trend in GraphML in 2022 -- particularly when applied to drug discovery, molecules and conformer generation, and quantum chemistry in general. Often, they are paired with the latest advancements in equivariant GNNs. Let's recapitulate the basics of diffusion models using the example of the Equivariant Diffusion paper by Hoogeboom et al using as few equations as possible The work introduces an equivariant diffusion model (EDM) for molecule generation that has to maintain E(3) equivariance over atom coordinates x (as to rotation, translation, reflection) and while node features h (such as atom types) remain invariant.