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 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.
@inproceedings{laabid2025diffalign,title={Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models},author={Laabid, Najwa and Rissanen, Severi and Heinonen, Markus and Solin, Arno and Garg, Vikas},booktitle={The Thirteenth International Conference on Learning Representations},year={2025},url={https://openreview.net/forum?id=onIro14tHv},}
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.
@inproceedings{laabid2024aligned,title={Aligned Diffusion Models for Retrosynthesis},author={Laabid, Najwa and Rissanen, Severi and Heinonen, Markus and Solin, Arno and Garg, Vikas},booktitle={ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling},year={2024},url={https://openreview.net/forum?id=fcF0Kal3Tc},}
@inproceedings{tamir2024conditional,title={Conditional Flow Matching for Time Series Modelling},author={Tamir, Ella and Laabid, Najwa and Heinonen, Markus and Garg, Vikas and Solin, Arno},booktitle={ICML 2024 Workshop on Structured Probabilistic Inference and Generative Modeling},year={2024},url={https://openreview.net/forum?id=Hqn4Aj7xrQ},}