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Graph Diffusion that can Insert and Delete
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Proposes GrIDDD, a discrete graph diffusion model that monotonically inserts and deletes atoms during denoising so the graph size adapts dynamically, evaluated on QM9/ZINC-250k property targeting and molecular optimization.
Problem
Discrete graph DDPMs keep the number of nodes fixed throughout diffusion, which hinders size-dependent conditional generation (e.g., molecular weight targeting) and property optimization that requires changing molecular size.
Approach
Reformulates discrete graph diffusion so nodes are monotonically deleted (via an auxiliary DEL type plus transient DEL* type for reinsertion) or inserted (activated at a sampled timestep with marginal-sampled labels) during forward and reverse processes, with the denoiser predicting node activation times and an auxiliary network predicting the number of DEL* nodes.
Key results
- On QM9, GrIDDD improves dipole moment MAE to 0.66 vs 0.74 for FreeGress (14%) and reaches 94% validity on HOMO vs 90.1% for FreeGress.
- On ZINC-250k molecular weight targeting, GrIDDD achieves MAE 4.89 vs 8.96 for FreeGress and 84.2% validity.
- On property optimization, GrIDDD reaches 45.1% QED success rate versus 9.4% for GCPN and LogP improvement 2.70 vs 2.49 for GCPN at sim >= 0.4.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GrIDDD instead of FreeGress for μ targeting | QM9 property targeting · QM9 (μ) | MAE: 0.74 $\pm$ 0.08 -> 0.66 $\pm$ 0.07 | Helped |
| use GrIDDD instead of FreeGress for μ targeting | QM9 property targeting · QM9 (μ) | validity: 83.7 $\%$ -> 79.0 $\%$ | Hurt |
| use GrIDDD instead of FreeGress for HOMO targeting | QM9 property targeting · QM9 (HOMO) | validity: 90.1 $\%$ -> 94 $\%$ | Helped |
| use GrIDDD instead of FreeGress for HOMO targeting | QM9 property targeting · QM9 (HOMO) | MAE: 0.32 $\pm$ 0.04 -> 0.37 $\pm$ 0.07 | Hurt |
| use GrIDDD instead of FreeGress for LogP targeting | ZINC-250k property targeting · ZINC-250k (LogP) | MAE: 0.17 $\pm$ 0.01 -> 0.19 $\pm$ 0.02 | Hurt |
| use GrIDDD instead of FreeGress for LogP targeting | ZINC-250k property targeting · ZINC-250k (LogP) | validity: 84.9 $\%$ -> 87.9 $\%$ | Helped |
| use GrIDDD instead of FreeGress for MW targeting with adaptive graph size | ZINC-250k property targeting · ZINC-250k (MW) | MAE: 8.96 $\pm$ 1.93 -> 4.89 $\pm$ 0.57 | Helped |
| use GrIDDD instead of GCPN | ZINC-250k molecular optimization · ZINC-250k (QED, similarity ≥ 0.4) | success rate: 9.4 $\%$ -> 45.1 $\%$ | Helped |
| disable insertions and deletions (ablation) | GrIDDD · ZINC-250k (QED optimization) | success rate: 45.1 $\%$ -> 33.8$\%$ | Hurt |
| disable insertions and deletions (ablation) | GrIDDD · ZINC-250k (LogP and DRD2 optimization) | success rate | No clear effect |
| start sampling with latents of size 2 (ablation) | GrIDDD on ZINC-250k LogP targeting · ZINC-250k (LogP; 128 samples) | sampling time: 152.05s -> 68.09s | Helped |
| start sampling with latents of size 24 (ablation) | GrIDDD on ZINC-250k LogP targeting · ZINC-250k (LogP; 128 samples) | sampling time: 152.05s -> 120.19s | Helped |
Surprising findings
- Naive padding-based implicit insertion/deletion in DiGress yields more disconnected graphs and worse cross-entropy than GrIDDD, despite similar validity.
- Disabling insertions and deletions drops QED optimization success to 33.8%, suggesting size control drives gains on QED.
Limitations
- Insertion and deletion can occasionally conflict at the same timestep, which is theoretically illegal in the framework.
- Generated molecules are more often split into multiple connected components than DiGress and FreeGress.
- Training is about 27-33% slower than FreeGress.
Experimental setup
Datasets: QM9 ZINC-250k
Benchmarks: QM9 ZINC-250k property optimization test suite (LogP, QED, DRD2)
Metrics: MAE validity improvement success rate diversity connected components validation cross-entropy
Baselines: DiGress FreeGress JT-VAE CG-VAE GCPN EDM-SyCo Unconditional
Builds on: DiGress FreeGress MiDi absorbing diffusion classifier-free guidance
Closest papers by meaning
- Graph Diffusion Transformers for Multi-Conditional Molecular Generation (NeurIPS 2024 · similarity 0.91)
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.90)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.90)
- Chain-of-Generation: Progressive Latent Diffusion for Text-Guided Molecular Design (NeurIPS 2026 · similarity 0.89)
- SubgDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learning (NeurIPS 2024 · similarity 0.89)
- DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform (NeurIPS 2025 · similarity 0.89)
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