Gromov-Monge Flow Matching for Equivariant Graph Generation

Graphs are invariant under node permutations, motivating the use of permutation-equivariant architectures in generative models. In flow matching, however, symmetry may also enter the source--target coupling: once graph pairs are compared up to node relabeling, the natural Wasserstein geometry is that of the graph quotient space. The Euclidean quotient metric of this space coincides with the Gromov--Monge distance, obtained by optimally relabeling the nodes. We develop this perspective theoretically, showing that quotient couplings can be lifted to aligned representatives without additional cost and that symmetrization yields equivariant flow-matching minimizers, including for categorical endpoint prediction. In practice, exact Gromov--Monge alignment is intractable, so we construct minibatch couplings using efficient Gromov--Wasserstein-type relaxations and lower bounds for the inner node alignment, optionally combined with an outer assignment between graphs. The resulting procedure changes only the training coupling and is compatible with standard permutation-equivariant architectures. Across continuous graph and categorical molecular generation, these structure-aware couplings substantially improve sample quality at small integration budgets, while our scaled-up molecular models remain competitive under conventional many-step sampling.

Parallel Noising in Neural Markov Logic Networks

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.