Gromov-Monge Flow Matching: symmetry-aware couplings boost graph generation at low step budgets
chaumian · x · 2026-08-31
A new arXiv paper, "Gromov-Monge Flow Matching for Equivariant Graph Generation" (Piening & Wald), argues that in flow matching for graphs, source-target couplings should be compared up to node relabeling; the natural Wasserstein geometry is then the Euclidean quotient metric of the graph quotient space, which coincides with the Gromov-Monge distance obtained by optimal node relabeling.
Theoretically, the authors show quotient couplings lift to aligned representatives at no extra cost, and that symmetrization yields equivariant flow-matching minimizers, including for categorical endpoint prediction. Since exact Gromov-Monge alignment is intractable, they build minibatch couplings via efficient Gromov-Wasserstein-type relaxations and lower bounds for inner node alignment, optionally with an outer assignment between graphs. The method only changes the training coupling and works with standard permutation-equivariant architectures.
On continuous graph and categorical molecular generation, these structure-aware couplings substantially improve sample quality at small integration budgets, while scaled-up molecular models remain competitive under conventional many-step sampling.
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