Graph generative models can be classified into two prominent families: one-shot models, which generate a graph in one go, and sequential models, which generate a graph by successive additions of nodes and edges. Ideally, between these two extreme models lies a continuous range of models that adopt different levels of sequentiality. This paper proposes a graph generative model, called Insert-Fill-Halt (IFH), that supports the specification of a sequentiality degree. IFH is based upon the theory of Denoising Diffusion Probabilistic Models (DDPM), designing a node removal process that gradually destroys a graph. An insertion process learns to reverse this removal process by inserting arcs and nodes according to the specified sequentiality degree. We evaluate the performance of IFH in terms of quality, run time, and memory, depending on different sequentiality degrees. We also show that using DiGress, a diffusion-based one-shot model, as a generative step in IFH leads to improvement to the model itself, and is competitive with the current state-of-the-art.
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