# Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models

arXiv: https://arxiv.org/abs/2405.17656 · HTML: https://mlsanity.com/paper/2405.17656/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 49 of its 80 references that are in the map.
- First posted on arXiv 27 May 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Molecular Transformer - A Model for Uncertainty-Calibrated Chemical Reaction Prediction](https://mlsanity.com/paper/1811.02633/) (2018)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Retrosynthesis Prediction with Conditional Graph Logic Network](https://mlsanity.com/paper/2001.01408/) (2020)
- [Predicting Organic Reaction Outcomes with Weisfeiler-Lehman Network](https://mlsanity.com/paper/1709.04555/) (2017)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [Molecule Edit Graph Attention Network: Modeling Chemical Reactions as Sequences of Graph Edits](https://mlsanity.com/paper/2006.15426/) (2020)
- [A Graph to Graphs Framework for Retrosynthesis Prediction](https://mlsanity.com/paper/2003.12725/) (2020)

## Built on by (most cited first, 8 of 8)

- [RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesis](https://mlsanity.com/paper/2506.04439/) (2025)
- [Diffusion Twigs with Loop Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2410.24012/) (2024)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal scheduling](https://mlsanity.com/paper/2608.28949/) (2026)
- [Representation-Guided Discrete Molecular Graph Retrosynthesis](https://mlsanity.com/paper/2605.24428/) (2026)
- [RetroGEF: Dynamic Graph Edit Flow for Single-Step Retrosynthesis](https://mlsanity.com/paper/2609.38484/) (2026)
- [Coverage Before Control: Route-Instruction Grounding and Steering for Controllable Retrosynthesis](https://mlsanity.com/paper/2609.39955/) (2026)
- [Your Discrete Graph Diffusion Model is Secretly Memorizing](https://mlsanity.com/paper/2610.13786/) (2026)

## Abstract (arXiv)

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. Code is available at https://github.com/Aalto-QuML/DiffAlign.