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About this paper
Yoann Boget, Pablo Strasser, Alexandros Kalousis
Hierarchical Discrete Flow Matching (HDFM) introduces a graph generative model that combines a novel D-Min clustering coarsening strategy with discrete flow matching, which significantly reduces generation time and computational cost while improving modeling performance across various graph datasets. The approach achieved competitive or superior performance on benchmarks like QM9H and SBM20k, reducing generation time by up to 5x compared to dense DFM, and demonstrated scalability to large graphs with up to 1500 nodes.
Key insights
- Explicitly minimizing the density of expanded graphs during the coarsening process significantly enhances the efficiency of hierarchical graph generation by constraining the refinement task to sparser structures.
- Combining hierarchical preprocessing with discrete flow matching effectively addresses both computational scaling (O(n²)) and the number of function evaluations (NFE), making graph generation faster and more scalable.
- The permutation-equivariant hierarchical framework naturally supports conditional generative modeling, allowing for guided graph design based on desired global structural properties.
Summary by alphaXiv.
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