Graph Generation

Discrete graph generation has emerged as a powerful paradigm for modeling graph-structured data, yet state of the art models often rely on Graph Transformers or higher order architectures. We revisit this design assumption by introducing GenGNN, a modular message passing backbone for graph generation. GenGNN enables powerful generation by persisting edge fields through latent refinement of coupled node edge graph states, all without requiring global attention. Diffusion models integrating GenGNN achieve over 90 percent validity on standard benchmark datasets, performing within margins of Graph Transformer backbones and achieving up to 2x or even 5x faster inference. Systematic ablations isolate how GenGNN is resilient to oversmoothing during generative denoising, indicating each GenGNN component is necessary for downstream generation quality. Finally, representation-space analysis suggests GenGNN learns functionally similar representations to more theoretically-expressive architectures; even at deeper layers. As such, GenGNN uplifts local message-passing to challenge prevailing assumptions that performant discrete graph generation requires global attention or higher-order representations. Source Code Available Here

Graph generation aims to sample discrete node and edge attributes while satisfying coupled structural constraints. Diffusion models for graphs often adopt largely factorized forward-noising, and many flow-matching methods start from factorized reference noise and coordinate-wise interpolation, so node-edge coupling is not encoded by the generative geometry and must be recovered implicitly by the core network, which can be brittle after discrete decoding. Bayesian Flow Networks (BFNs) evolve distribution parameters and naturally support discrete generation. But classical BFNs typically rely on factorized beliefs and independent channels, which limit geometric evidence fusion. We propose Variational Bayesian Flow Network (VBFN), which performs a variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions. Each Bayesian update reduces to solving a symmetric positive definite linear system, enabling coupled node and edge updates within a single fusion step. We construct sample-agnostic sparse precisions from a representation-induced dependency graph, thereby avoiding label leakage while enforcing node-edge consistency. On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods. The reproducible code is available at https://github.com/Cello2195/VBFN.

Diffusion models have demonstrated remarkable generative capabilities in continuous data domains such as images and videos. Recently, discrete graph diffusion models (DGDMs) have extended this success to graph generation, achieving state-of-the-art performance. However, deploying DGDMs in safety-critical applications, such as drug discovery, poses significant risks without a thorough understanding of their security vulnerabilities. In this work, we conduct the first study of backdoor attacks on DGDMs, a potent threat that manipulates both the training and generation phases of graph diffusion. We begin by formalizing the threat model and then design a backdoor attack that enables the compromised model to: 1) generate high-quality, benign graphs when the backdoor is not activated, 2) produce effective, stealthy, and persistent backdoored graphs when triggered, and 3) preserve fundamental graph properties (permutation equivariance and exchangeability) even under attack. We validate 1) and 2) empirically, both with and without backdoor defenses, and support 3) through theoretical analysis inspired by prior work.