GraphonFlow: Learning Latent Graphon Distributions for Structure-Preserving Graph Generation

Graph generative models must capture complex structural dependencies while preserving domain-specific constraints. However, existing flow-based approaches typically initialise generation from independent noise or fixed priors, leaving the flow model to recover much of the target structure during generation. We propose GraphonFlow, a probabilistic framework that learns a latent-conditioned structured source distribution for flow-based graph generation. Our key idea is to integrate latent graph representation learning with graphon modelling, providing an informative structural starting point for subsequent flow learning. A two-stage training strategy first learns the latent representation and graphon-based source, and then freezes this source while learning a conditional velocity field that transforms structured source samples toward target graphs. To support structure-preserving generation, GraphonFlow further incorporates canonical graph representations for consistent graphon learning and connectivity-aware regularisation across the generative process. Experiments on four molecular benchmarks and three synthetic graph families demonstrate competitive performance in chemical validity, diversity, and structural fidelity. Extensive ablations further demonstrate the importance of the learned graphon source, canonical representation, two-stage optimisation, and connectivity-aware learning. Overall, our results show that learning the source distribution itself provides an effective alternative to initialising graph flows from unstructured or fixed priors.