  Retrosynthesis, the task of identifying precursors for a given molecule, can
be naturally framed as a conditional graph generation task. Diffusion models
are a particularly promising modelling approach, enabling post-hoc conditioning
and trading off quality for speed during generation. 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. Our new denoiser achieves the highest top-$1$
accuracy ($54.7$\%) across template-free and template-based methods on
USPTO-50k. We also demonstrate the ability for flexible post-training
conditioning and good sample quality with small diffusion step counts,
highlighting the potential for interactive applications and additional controls
for multi-step planning.
