Flowette: Flow Matching with Graphette Priors for Graph Generation

TL;DR

Flowette introduces a novel flow-based graph generative model that incorporates structural priors called graphettes, achieving state-of-the-art results on synthetic and molecular graph benchmarks.

Contribution

The paper proposes Flowette, a flow matching framework with graphette priors for improved graph generation, combining optimal transport and regularization techniques.

Findings

Flowette attains state-of-the-art performance on multiple graph benchmarks.

Incorporating graphette priors enhances structural fidelity in generated graphs.

The framework effectively combines structural priors with flow-based training methods.

Abstract

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs a graph neural network-based transformer to learn a velocity field over graph representations with node and edge attributes. Our model promotes topology-aware alignment through optimal transport-based coupling and encourages global structural coherence through regularisation. To incorporate domain-driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs such as rings, stars, and trees. We theoretically analyze the coupling, invariance, and structural properties of the framework, evaluate it on synthetic and molecular benchmarks, and isolate the contributions of the structural prior, the optimal-transport coupling, and the regularisation terms through controlled ablations. Flowette achieves competitive performance overall, attaining state-of-the-art results on several metrics across multiple benchmarks, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.