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Life sciences · Preprint
arXiv · September 4, 2026
Posted before peer review. The findings may change or fail to hold.
This is a preprint describing Embedded Graph Flows (EGF), a machine learning method for generating discrete categorical graphs by learning continuous embeddings and using permutation-equivariant transport. The work is computational and algorithmic; it reports benchmark performance on molecular graph datasets but contains no clinical data, patient outcomes, or evidence relevant to medical practice.
Preprint. Intervention: Embedded Graph Flows (EGF): a generative model learning continuous embeddings for node and edge categories, transporting Gaussian noise via permutation-equivariant graph transformer, with terminal readout to discrete categories.. Compared with: DiGress (categorical-diffusion baseline) and GruM (bridge-based baseline) on QM9 and ZINC250k benchmarks..
On QM9 molecular benchmark, EGF achieved Fréchet ChemNet Distance (FCD) of 0.150, lower than DiGress baseline (0.717) and GruM baseline (0.812) On ZINC250k larger-molecule dataset, EGF retained lowest maximum mean discrepancy (MMD) using neighbourhood subgraph pairwise distance kernel (NSPDK)
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This is an unrefereed technical preprint describing a machine learning algorithm for graph generation with benchmark comparisons, not a clinical study, and carries no evidence for clinical practice.
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Generating categorical graphs requires choosing node and edge types that form a coherent structure without depending on node order. Many graph generators encode categories as fixed one-hot vectors, which can impose an artificial geometry in which categories are equidistant. We propose Embedded Graph Flows (EGF), a generative model that learns continuous embeddings for node and unordered-edge categories and transports Gaussian noise towards these learnt endpoints using a permutation-equivariant graph transformer. A terminal readout maps the embeddings back to discrete graph categories. Across molecular benchmarks, EGF achieved competitive performance. On QM9, EGF gives the best result on all four reported metrics among the three methods, including a Fréchet ChemNet Distance (FCD) of 0.150, compared with 0.717 for the categorical-diffusion baseline DiGress and 0.812 for the bridge-based baseline GruM. When applied to larger molecules in ZINC250k, EGF retains the lowest maximum mean discrepancy (MMD) using the neighbourhood subgraph pairwise distance kernel (NSPDK), indicating close agreement with the local substructures of the reference molecules. Our code is available at https://github.com/Trusted-System-Lab/EGF.
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