Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in other applications such as tabular and graph data generation. However, due to computational complexity, to this date, the application of these techniques to graph data has been restricted to small graphs, such as those used in molecular modeling. In this paper, we propose SaGess, a discrete denoising diffusion approach, which is able to generate large real-world networks by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. The algorithm is capable of generating larger graphs by sampling a covering of subgraphs of the initial graph in order to train DiGress. SaGess then constructs a synthetic graph using the subgraphs that have been generated by DiGress. We evaluate the quality of the synthetic data sets against several competitor methods by comparing graph statistics between the original and synthetic samples, as well as evaluating the utility of the synthetic data set produced by using it to train a task-driven model, namely link prediction. In our experiments, SaGess, outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor, both on the graph metrics and on the link prediction task.

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