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Smooth Interpolation for Improved Discrete Graph Generative Models

ICML 2025 · Graph learning › Graph self-supervised learning · approach: Diffusion-based graph generation

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Proposes GraphBFN, a Bayesian Flow Network for discrete graph generation that models graph topology via a continuous probabilistic adjacency matrix, with adaptive Flowback sampling and a generalized accuracy schedule.

Problem

Discrete graph diffusion models face unbalanced, topology-distorting corruption steps; the goal is a smoother generative process for discrete graphs (abstract and molecular) that preserves graph topology during generation.

Approach

Replaces discrete noisy states with continuous count-based latents from Bayesian Flow Networks, yielding a probabilistic adjacency matrix whose spectrum evolves smoothly; adds adaptive Flowback sampling, a general accuracy schedule compatible with informative priors, and spectrum conditioning on output distributions for large graphs.

Key results

• On ZINC250k GraphBFN reaches FCD 2.116 and Scaffold 0.5304, beating GruM (2.257, 0.5299).
• On Planar GraphBFN achieves V.U.N. 96.7%, vs 90.0% for GruM and 75.0% for DiGress.
• With 25 or 50 sampling steps GraphBFN matches diffusion models using 500 or 1000 steps (over 10x sampling efficiency gain).

Measured effects reported in the paper

Surprising findings

• Vanilla BFN sampling on Planar gives only 14.8% V.U.N., showing the train-test discrepancy problem that adaptive Flowback fixes.
• GraphBFN shows a slight drop in novelty on MOSES (89.0%) versus other one-shot models, which the authors attribute to overlap with the training distribution.

Limitations

• Spectrum conditioning is only used on large graphs such as SBM, not uniformly applied.
• Novelty drops slightly on MOSES relative to other one-shot models, suggesting overlap with training distribution.

Experimental setup

Datasets: Planar SBM QM9 ZINC250k MOSES

Benchmarks: Planar SBM QM9 with explicit hydrogen QM9 implicit hydrogen ZINC250k MOSES

Metrics: MMD degree MMD clustering MMD orbit MMD spectrum V.U.N. Valid FCD NSPDK Scaffold similarity Atom stability

Baselines: DiGress GruM GBD GDSS EDP-GNN SPECTRE GraphRNN GRAN JT-VAE GraphAF MoFlow GraphDF

Builds on: Bayesian Flow Networks DiGress discrete diffusion (D3PM) self-conditioning

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