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
Embedded Graph Flows (EGF) is a generative model for categorical graphs that learns continuous embeddings for node and unordered-edge categories and uses a permutation‑equivariant graph transformer to transport Gaussian noise toward these embeddings. A terminal readout then maps the embeddings back to discrete graph categories. EGF achieves competitive performance on molecular benchmarks, outperforming other methods on QM9 and maintaining low maximum mean discrepancy on ZINC250k.
By Ethan Ma, Zihan Wang, Chris Siu Yeung Chow, Xinguo Feng, Qingqing Li, Rui Jiang, Naipeng Dong, Guangdong Bai
arXiv:2607. 19083v1 Announce Type: new Abstract: Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes.
By Daniele Angioletti, Marco Nobile, Vittorio Limongelli
arXiv:2602. 18084v2 Announce Type: replace Abstract: Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs.
By Benjamin Honor\'e, Alba Carballo-Castro, Yiming Qin, Pascal Frossard
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
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:2609.15437v1 Announce Type: cross
Abstract: End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderin...
By Federico M\'endez, Paul Krzakala, Gabriel Melo, Charlotte Laclau, R\'emi Flamary, Florence d'Alch\'e-Buc
arXiv:2602.23566v4 Announce Type: replace-cross
Abstract: We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs...
By Asiri Wijesinghe, Sevvandi Kandanaarachchi, Daniel M. Steinberg, Cheng Soon Ong
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
The paper introduces Equivariant-Free Transformer-Autoencoded Latent Flow Matching (EF‑TALFM), a two‑stage generative framework that uses a single fixed‑dimensional latent vector to produce variable‑size 3D molecules. The first stage samples the latent vector via flow matching, and the second stage employs an autoregressive Transformer decoder that determines molecule size while generating atom types, coordinates, and chemical states. EF‑TALFM outperforms prior methods on the PCQM4Mv2 benchmark, achieving higher uniqueness, novelty, and computational throughput, and its internal ranking improves the hit rate for target HOMO–LUMO gaps while maintaining novelty.
arXiv:2608.29635v1 Announce Type: new
Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
By Lutz Oettershagen, Honglian Wang, Aristides Gionis
arXiv:2605.06140v3 Announce Type: replace-cross
Abstract: Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such...
By Samir Darouich, Vinh Tong, Llu\'is Pastor-P\'erez, Tanja Bien, Loay Mualem, Mathias Niepert