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Flowette: Flow Matching with Graphette Priors for Graph Generation

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Diffusion-based graph generation · 0 citations (OpenAlex)

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Flowette applies rectified flow matching to attributed graphs with FGW-based Hungarian coupling, endpoint and chemistry regularizers, and graphette priors (graphons extended with ring/star/tree edits) for graph generation.

Problem

Graph generation with recurring subgraph motifs (rings, stars, trees) where existing flow-matching approaches use implicit or independent noise-data coupling and generic priors, leading to high-variance velocity supervision and poor structural fidelity.

Approach

Couple noise and data graphs via fused Gromov-Wasserstein distance with Hungarian batch matching, train a permutation-aware edge-conditioned GNN-transformer velocity field with endpoint consistency and chemistry-aware regularizers, and use graphettes (graphon sparsification plus graph edit functions such as ring or star addition) as structured source distributions.

Key results

• On QM9, Flowette reports 99.81% validity and 99.30% uniqueness with NSPDK 0.0003, while on ZINC250K it reports 99.90% validity and 0.0006 NSPDK.
• On Guacamol, Flowette reaches 98.0 V.U.N. and 97.9 KL divergence, with 98.6 validity (DeFoG reports 99.0 validity).
• On MOSES, Flowette reports 98.10 novelty, the highest among compared methods, with SNN 0.58 and scaffold 15.3.

Surprising findings

• Synthetic performance remains strong without chemistry-aware regularizers (reported 100% V.U.N. on Tree and SBM).
• Paper reports FGW coupling precomputation cost of O(B^2 n^3), amortised offline.

Limitations

• FGW coupling adds O(B^2 n^3) precomputation cost that may limit scalability.
• Graphette specification relies on coarse domain knowledge (rings, hubs, trees) chosen by the user.
• Chemistry-aware regularizers are domain-specific, and a discrete projection step at generation time may introduce artefacts.

Experimental setup

Datasets: Tree SBM Ego-small QM9 ZINC250K Guacamol MOSES

Benchmarks: QM9 ZINC250K Guacamol MOSES Tree SBM Ego-small

Metrics: Validity Uniqueness NSPDK V.U.N. KL divergence Novelty SNN Scaffold similarity Degree Clustering

Baselines: EDP-GNN GraphARM DiGress GDSS GruM GraphBFN SID DeFoG GBD DisCo Cometh G2PT

Builds on: flow matching rectified flow DiGress DeFoG graphons graphexes fused Gromov-Wasserstein

Closest papers by meaning

• Smooth Interpolation for Improved Discrete Graph Generative Models (ICML 2025 · similarity 0.88)
• Variational Flow Matching for Graph Generation (NeurIPS 2024 · similarity 0.87)
• DeFoG: Discrete Flow Matching for Graph Generation (ICML 2025 · similarity 0.87)
• DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation (NeurIPS 2026 · similarity 0.87)
• Geometric Generative Modeling with Noise-Conditioned Graph Networks (ICML 2025 · similarity 0.86)
• Structured Coupling for Flow Matching (NeurIPS 2026 · similarity 0.86)