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Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models
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Shows that permutation-equivariant graph diffusion denoisers fail on identity (copy) reactions and proposes aligned permutation equivariance via atom-mapping-based inputs, achieving SOTA top-1 among template-free methods for retrosynthesis on USPTO-50k.
Problem
Standard permutation-equivariant graph diffusion denoisers cannot copy a conditioning graph (identity reaction), limiting graph-to-graph translation such as single-step retrosynthesis.
Approach
Relax permutation equivariance to aligned permutation equivariance by feeding atom-mapping information into the denoiser (via atom-mapped positional encodings, a direct product-to-output skip connection, or input concatenation), so the network can break symmetries and copy the product structure while staying equivariant elsewhere.
Key results
- DiffAlign-PE+skip reaches 54.7% top-1 on USPTO-50k, the best top-1 across all listed methods including template-based.
- The unaligned permutation-equivariant denoiser reaches only 4.1% top-1 (MRR 0.056).
- DiffAlign-PE+skip gets MRR 0.639, state-of-the-art among template-free methods on top-k>1 and MRR as claimed.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Align the product and reactant graphs using atom-mapping information | Graph diffusion denoiser · USPTO-50k test | top-1 accuracy: 4.1 -> 44.1 | Helped |
| Add atom-mapped positional encodings instead of input alignment (ablation) | DiffAlign model · USPTO-50k test | top-1 accuracy: 44.1 -> 49.0 | Helped |
| Add an output skip connection carrying the aligned product graph (ablation) | DiffAlign-PE · USPTO-50k test | top-1 accuracy: 49.0 -> 54.7 | Helped |
| Add an output skip connection carrying the aligned product graph (ablation) | DiffAlign-PE · USPTO-50k test | MRR: 0.601 -> 0.639 | Helped |
| Use absorbing-state transitions instead of uniform or marginal transitions (ablation) | Graph diffusion model · USPTO-50k | model performance | Helped |
Surprising findings
- Permutation-equivariant denoisers provably converge to marginal 'mean' outputs on identity reactions at high noise, so they fail to copy the product even though copying is easy.
- Aligned denoisers can recover the ground truth even with a single denoising step, while unaligned models drop to near zero top-k at 10 steps.
Limitations
- Requires atom-mapping information, which may be imperfect or unavailable.
- High computational demand; likely slower than template-based models.
Experimental setup
Datasets: USPTO-50k
Benchmarks: USPTO-50k
Metrics: top-k accuracy mean reciprocal rank
Baselines: Retrosym GLN LocalRetro Retrocomposer RetroKNN G2G GraphRetro MEGAN RetroDiff MARS Graph2SMILES Retroformer
Builds on: discrete denoising diffusion (D3PM) graph transformer absorbing state diffusion DPS
Closest papers by meaning
- Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.88)
- Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.88)
- Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion (NeurIPS 2025 · similarity 0.87)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.87)
- Improving Equivariant Networks with Probabilistic Symmetry Breaking (ICLR 2025 · similarity 0.87)
- SymDrift: One-Shot Generative Modeling under Symmetries (NeurIPS 2026 · similarity 0.87)
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