Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models
Najwa Laabid Severi Rissanen Markus Heinonen Arno Solin Vikas Garg
Graph diffusion models, dominant in graph generative modeling, remain underexplored for graph-to-graph translation tasks like chemical reaction prediction. We demonstrate that standard permutation equivariant denoisers face fundamental limitations in these tasks due to their inability to break symmetries in noisy inputs. To address this, we propose \emph{aligning} input and target graphs to break input symmetries while preserving permutation equivariance in non-matching graph portions. Using retrosynthesis (i.e., the task of predicting precursors for synthesis of a given target molecule) as our application domain, we show how alignment dramatically improves discrete diffusion model performance from $5$\% to a SOTA-matching $54.7$\% top-1 accuracy. Code is available at https://github.com/Aalto-QuML/DiffAlign.
Graph Diffusion, Discrete Diffusion, Equivariance, Symmetries
We propose aligned permutation equivariance in order to break the symmetries of equivariant denoisers in graph diffusion.