Alignment Matters Inside and Out in Equivariant Graph Flow Matching
Graphs are invariant under node permutations, motivating permutation-equivariant architectures in generative models. In flow matching, however, symmetry also affects the source-target coupling: one must choose both which graphs to pair and which node representatives to align. We study these two forms of alignment, termed outer and inner alignment, and their effect on equivariant graph flow matching. We connect inner alignment to transport on the graph quotient space, whose Euclidean quotient metric coincides with Gromov-Monge distance, and show that quotient couplings admit aligned representative lifts while symmetrization yields equivariant flow-matching minimizers, including for categor...
| Authors | Moritz Piening, Christian Wald |
|---|---|
| Primary category | cs.LG |
| Published | 27 August 2026 |
| Last updated at source | 29 September 2026 |
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