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Graph Generation with Diffusion Mixture
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Proposes GruM, a graph diffusion model that learns the final graph (graph mixture) of a mixture of endpoint-conditioned OU bridge processes, trained simulation-free by maximum likelihood, and evaluated on general graph, 2D molecule and 3D molecule generation.
Problem
Denoising graph diffusion models learn score or noise and do not explicitly model the final graph topology, leading to invalid graphs; prior bridge/mixture methods learn drifts that diverge near terminal time and cannot handle discrete structure well.
Approach
Construct the generative process as a mixture of Ornstein-Uhlenbeck bridge processes whose drift is driven toward a weighted mean of data graphs (the graph mixture), and train a network to predict that graph mixture with a simulation-free graph mixture matching objective that upper-bounds KL and maximizes likelihood.
Key results
- On general graph generation, GruM reaches 90% V.U.N. on Planar and 85% on SBM, outperforming DiGress (75 and 74).
- On ZINC250k 2D molecule generation, GruM achieves 98.65% validity and FCD 2.257 versus DiGress's 94.99% and 3.482.
- GruM trains about 17.5 times faster than SDE-simulation-based training and achieves non-zero molecule stability on GEOM-DRUGS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GruM rather than DiGress | Planar graph generation · Planar | V.U.N.: 75 -> 90.0 | Helped |
| Use GruM rather than DiGress | SBM graph generation · SBM | V.U.N.: 74 -> 85.0 | Helped |
| Use GruM rather than SPECTRE | Proteins graph generation · Proteins | Spec. MMD: 0.0052 -> 0.0030 | Helped |
| Use GruM rather than DiGress | QM9 molecule generation · QM9 | Validity (%): 98.19 -> 99.69 | Helped |
| Use GruM rather than DiGress | QM9 molecule generation · QM9 | FCD: 0.095 -> 0.108 | Hurt |
| Use GruM rather than DiGress | QM9 molecule generation · QM9 | NSPDK MMD: 0.0003 -> 0.0002 | Helped |
| Use GruM rather than DiGress | QM9 molecule generation · QM9 | Scaffold similarity: 0.9353 -> 0.9449 | Helped |
| Use GruM rather than GDSS | ZINC250k molecule generation · ZINC250k | Validity (%): 97.01 -> 98.65 | Helped |
| Use GruM rather than DiGress | ZINC250k molecule generation · ZINC250k | FCD: 3.482 -> 2.257 | Helped |
| Add an output-layer transformation that exploits graph inductive bias (ablation) | GruM · Planar | model complexity (Jacobian Frobenius norm) | Helped |
| Train with graph-mixture matching rather than SDE simulation | GruM · Graph generation training | training speed: 17.5 times faster | Helped |
| Early-stop the generative process after the destination mixture converges | GruM · Planar | generation time: up to 20% | Helped |
Surprising findings
- Early stopping of the generative process reduces generation time by up to 20% on the Planar dataset without large quality loss.
Limitations
- Generalization beyond graph-structured data (e.g., proteins, manifolds) is left as future work.
- Learning the drift performs poorly on general graph tasks, per the authors' appendix analysis.
- Potential misuse for generating toxic substances or narcotics is noted in the impact statement.
Experimental setup
Datasets: Planar SBM Proteins QM9 ZINC250k GEOM-DRUGS
Benchmarks: Planar SBM Proteins QM9 ZINC250k GEOM-DRUGS
Metrics: MMD degree MMD clustering MMD orbit MMD spectrum V.U.N. validity FCD NSPDK MMD scaffold similarity atom stability
Baselines: GraphRNN GRAN SPECTRE EDP-GNN GDSS ConGress DiGress MoFlow GraphAF GraphDF G-Schnet EN-Flow
Builds on: denoising diffusion models Doob's h-transform diffusion mixture representation Bridge (diffusion mixture) EDM
Closest papers by meaning
- Discrete-state Continuous-time Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.91)
- Smooth Interpolation for Improved Discrete Graph Generative Models (ICML 2025 · similarity 0.90)
- Advancing Graph Generation through Beta Diffusion (ICLR 2025 · similarity 0.90)
- Graph Diffusion that can Insert and Delete (NeurIPS 2025 · similarity 0.90)
- Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation (ICML 2025 · similarity 0.90)
- Generating Graphs via Spectral Diffusion (ICLR 2025 · similarity 0.90)
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