In a 9 October arXiv preprint, researchers study a discrete graph diffusion model trained on a single graph using synthetic two-community stochastic block models. Their term “conditional memorization” describes a tendency for reverse diffusion to restore edges from a corrupted training graph when given that graph as its starting point; the same degree of recovery did not appear for an unseen test graph in the corresponding probe. The first page lists author Adarsh Jamadandi’s affiliation with CNRS and IRISA in France.

In the authors’ reported experiment with 256 nodes, after 60% of edges were corrupted, the model recovered 96.9% of training-graph edges, compared with 7.7% for a reference method that knew only the generating probability law. This is a measurement within the paper’s synthetic setup, not evidence of leakage in real datasets or of identical behavior across all graph-generation models. The authors also report that checkpoints developing community structure came after the onset of this memorization, so early stopping did not separate the two stages. The results suggest that metrics comparing only generated samples may miss training-data bias.