Gromov-Monge Flow Matching for Equivariant Graph Generation

• URL: http://arxiv.org/abs/2608.26961v1
• Date: Thu, 27 Aug 2026 11:01:03 GMT
• Title: Gromov-Monge Flow Matching for Equivariant Graph Generation
• Abstract summary: In flow matching, symmetry may enter the source--target coupling.<n>We show that quotient couplings can be lifted to aligned representatives without additional cost.<n>We construct minibatch couplings using efficient Gromov--Wasserstein-type relaxations.
• Score: 3.3603088054104284
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Reinforcement Learning for Microcanonical Graph Ensemble with Assortativity Constraints [1.0896567381206717]
  How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties.<n>Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning framework that transforms any given graph through degree-preserving rewirings.
  arXiv  Detail & Related papers  (2026-05-22T06:57:41Z)
• Balancing Symmetry and Efficiency in Graph Flow Matching [33.80974796363154]
  We study the trade-off for graph generative models between strict equivariance and controllable symmetry modulation.<n>We show that properly modulating the symmetry signal can delay overfitting while accelerating convergence.
  arXiv  Detail & Related papers  (2026-02-20T09:17:57Z)
• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• Differentiable Tripartite Modularity for Clustering Heterogeneous Graphs [0.0]
  We introduce a differentiable formulation of tripartite modularity for graphs composed of three node types connected through mediated interactions.<n>Community structure is defined in terms of weighted co-paths across the tripartite graph, together with an exact factorized computation that avoids the explicit construction of dense third-order tensors.<n>We validate the proposed framework on large-scale urban cadastral data, where it exhibits robust convergence behavior and produces spatially coherent partitions.
  arXiv  Detail & Related papers  (2026-02-10T15:06:53Z)
• Variational Bayesian Flow Network for Graph Generation [54.94088904387278]
  We propose Variational Bayesian Flow Network (VBFN) for graph generation.<n>VBFN performs variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions.<n>On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.
  arXiv  Detail & Related papers  (2026-01-30T03:59:38Z)
• Scalable Graph Compressed Convolutions [68.85227170390864]
  We propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning.
  arXiv  Detail & Related papers  (2024-07-26T03:14:13Z)
• Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning [77.1421343649344]
  We propose a generalization of Transformers towards operating entirely on the product of constant curvature spaces. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges.
  arXiv  Detail & Related papers  (2023-09-08T02:44:37Z)
• Isometric Transformation Invariant and Equivariant Graph Convolutional Networks [5.249805590164902]
  We propose a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs. We demonstrate that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data.
  arXiv  Detail & Related papers  (2020-05-13T13:44:44Z)
• Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs [81.12344211998635]
  A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs) We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.
  arXiv  Detail & Related papers  (2020-03-11T17:21:15Z)
• Permutation Invariant Graph Generation via Score-Based Generative Modeling [114.12935776726606]
  We propose a permutation invariant approach to modeling graphs, using the recent framework of score-based generative modeling. In particular, we design a permutation equivariant, multi-channel graph neural network to model the gradient of the data distribution at the input graph. For graph generation, we find that our learning approach achieves better or comparable results to existing models on benchmark datasets.
  arXiv  Detail & Related papers  (2020-03-02T03:06:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.