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Diffusion Twigs with Loop Guidance for Conditional Graph Generation
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Proposes Twigs, a score-based diffusion framework with a trunk process for graph structure and stem processes for graph properties, coupled by a "loop guidance" sampling scheme, evaluated on conditional molecule and generic graph generation.
Problem
Conditional graph generation (e.g., molecules with target quantum/docking properties, or network graphs with target statistics) where existing classifier-based and classifier-free guidance do not model hierarchical dependencies between structure and properties.
Approach
Co-evolve a trunk diffusion over the graph structure with multiple stem diffusions over dependent properties, factorizing the joint score as trunk score plus per-property coupling scores, and alternate updates between stems and trunk during sampling ("loop guidance").
Key results
- On QM9 single-property conditioning, Twigs achieves lower MAE than JODO on all six properties (e.g., C_v 0.559 vs 0.581; alpha 1.36 vs 1.42).
- On ZINC250K novel top 5% docking score, Twigs is best on 4 of 5 targets (e.g., parp1 10.449 vs MOOD 10.409; 5ht1b 10.542 vs 10.487), with braf second to MOOD.
- On Community-small and Enzymes, Twigs gives lowest MAE across density, clustering, assortativity and transitivity conditioning (e.g., clustering 9.67 vs 10.6 for the best baseline on Community-small).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Twigs with loop-guided stem and trunk processes rather than JODO | Conditional QM9 single-property generation · QM9 single-property α | MAE: 1.42 \sstd{0.01} -> 1.36 \sstd{0.01} | Helped |
| Use Twigs with loop-guided stem and trunk processes rather than JODO | Conditional QM9 single-property generation · QM9 single-property μ | MAE: 0.628 \sstd{0.003} -> 0.627 \sstd{0.001} | No clear effect |
| Use Twigs with multiple stem processes rather than JODO | Conditional QM9 multiple-property generation · QM9 multiple-property combinations involving μ | MAE | Helped |
| Use Twigs rather than MOOD | ZINC250K molecule optimization · ZINC250K across parp1, fa7, 5ht1b, braf, and jak2 | Novel top 5% docking score | Mixed |
| Use Twigs rather than MOOD | ZINC250K molecule optimization · ZINC250K across parp1, fa7, 5ht1b, braf, and jak2 | Novel hit ratio | Mixed |
| Use Twigs rather than the compared graph-generation baselines | Conditional network graph generation · Community-small and Enzymes | MAE | Helped |
| Use three rather than one secondary diffusion flow (ablation) | Twigs · Community-small | Training time for 5,000 epochs: 0h 22m -> 0h 24m | Hurt |
| Use three rather than one secondary diffusion flow (ablation) | Twigs · Enzymes | Training time for 5,000 epochs: 6h 45m -> 6h 59m | Hurt |
| Use three rather than one secondary diffusion flow (ablation) | Twigs · Community-small and Enzymes | MAE | Helped |
Surprising findings
- Twigs' runtime per molecule is higher than MOOD (0.378 vs 0.267 seconds), a trade-off the authors accept for better property alignment.
Limitations
- Assumes conditional independence of stem properties given the structure, which may not hold in general.
- Multiple stem processes add parameters and training time.
- Only validated on graph/molecule tasks; effectiveness in image, text, or audio is untested.
Experimental setup
Datasets: QM9 ZINC250K Community-small Enzymes
Benchmarks: QM9 ZINC250K Community-small Enzymes
Metrics: MAE novel hit ratio novel top 5% docking score atom stability molecule stability novelty FCD KL divergence
Baselines: EDM EEGSDE GeoLDM EquiFM TEDMol JODO GDSS MOOD REINVENT MORLD HierVAE Digress
Builds on: GDSS EDM Score-based SDEs classifier-free guidance MOOD
Closest papers by meaning
- Discrete-state Continuous-time Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.88)
- DeFoG: Discrete Flow Matching for Graph Generation (ICML 2025 · similarity 0.88)
- Diffuse, Sample, Project: Plug-And-Play Controllable Graph Generation (ICML 2024 · similarity 0.88)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.88)
- TFG-Flow: Training-free Guidance in Multimodal Generative Flow (ICLR 2025 · similarity 0.87)
- Graph Diffusion Transformers for Multi-Conditional Molecular Generation (NeurIPS 2024 · similarity 0.87)
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