Aligned Diffusion Models for Retrosynthesis

Retrosynthesis, the task of identifying precursors for a given molecule, can be naturally framed as a conditional graph generation task, with diffusion models being a particularly promising approach. We show mathematically that permutation equivariant denoisers severely limit the expressiveness of graph diffusion models and thus their adaptation to retrosynthesis. To address this limitation, we relax the equivariance requirement such that it only applies to aligned permutations of the conditioning and the generated graphs obtained through atom mapping, resulting in a diffusion model with state-of-the-art results in template-free retrosynthesis.