The paper introduces Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
By Moritz Piening, Christian Wald
Transport-Coupled Bayesian Flows for Molecular Graph Generation (TopBF) addresses a key mismatch in existing diffusion models for molecular graph generation by eliminating the need for hard discretization during sampling. The framework generates graphs directly in continuous parameter distributions, learns graph topology via a Quasi-Wasserstein optimal‑transport coupling with geodesic costs, and enables property‑conditioned generation without retraining. Experiments on QM9 and ZINC250k show that TopBF achieves higher structural fidelity and more efficient generation compared to prior methods.
By Yida Xiong, Jiameng Chen, Kun Li, Hongzhi Zhang, Xiantao Cai, Lei Lei, Wenbin Hu
The paper investigates how alignment—both outer (choosing which graphs to pair) and inner (aligning node representatives)—affects permutation-equivariant graph flow matching. It connects inner alignment to transport on the graph quotient space and shows that quotient couplings can be lifted to aligned representatives, while symmetrization yields equivariant flow‑matching minimizers. Experiments on continuous graph and molecular generation demonstrate that appropriate alignment can simplify trajectories and improve few‑step generation, though the benefits vary with the type of alignment and computational budget.
By Moritz Piening, Christian Wald
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
By Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu
arXiv:2603. 23398v3 Announce Type: replace-cross Abstract: Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design.
By Michal Balcerak, Suprosanna Shit, Chinmay Prabhakar, Sebastian Kaltenbach, Michael S. Albergo, Yilun Du, Bjoern Menze
arXiv:2607. 21607v1 Announce Type: cross Abstract: Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks.
By Ranjan Veerabhadraswamy, Ajith Jubilson Emerson