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 diffusion models have gained significant attention in graph generation tasks, but they often inherit and amplify topology biases from sensitive attributes (e.g. gender, age, region), leading to unfair synthetic graphs. Existing fair graph generation using diffusion models is limited to specific graph-based applications with complete labels or requires simultaneous updates for graph structure and node attributes, making them unsuitable for general usage. To relax these limitations by applying the debiasing method directly on graph topology, we propose Fair Graph Diffusion Model (FairGDiff), a counterfactual-based one-step solution that mitigates topology biases while balancing fairness and utility. In detail, we construct a causal model to capture the relationship between sensitive attributes, biased link formation, and the generated graph structure. By answering the counterfactual question "Would the graph structure change if the sensitive attribute were different?", we estimate an unbiased treatment and incorporate it into the diffusion process. FairGDiff integrates counterfactual learning into both forward diffusion and backward denoising, ensuring that the generated graphs are independent of sensitive attributes while preserving structural integrity. Extensive experiments on real-world datasets demonstrate that FairGDiff achieves a superior trade-off between fairness and utility, outperforming existing fair graph generation methods while maintaining scalability.

Large language model (LLM)-based multi-agent systems have shown strong capabilities in tasks such as code generation and collaborative reasoning. However, the effectiveness and robustness of these systems critically depend on their communication topology, which is often fixed or statically learned, ignoring real-world dynamics such as model upgrades, API (or tool) changes, or knowledge source variability. To address this limitation, we propose CARD (Conditional Agentic Graph Designer), a conditional graph-generation framework that instantiates AMACP, a protocol for adaptive multi-agent communication. CARD explicitly incorporates dynamic environmental signals into graph construction, enabling topology adaptation at both training and runtime. Through a conditional variational graph encoder and environment-aware optimization, CARD produces communication structures that are both effective and resilient to shifts in model capability or resource availability. Empirical results on HumanEval, MATH, and MMLU demonstrate that CARD consistently outperforms static and prompt-based baselines, achieving higher accuracy and robustness across diverse conditions. The source code is available at: https://github.com/Warma10032/CARD.

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs a graph neural network-based transformer to learn a velocity field over graph representations with node and edge attributes. Our model promotes topology-aware alignment through optimal transport-based coupling and preserves structural fidelity through endpoint- and chemistry-aware regularisation. To incorporate domain-driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs such as rings, stars, and trees. We theoretically analyze the coupling, invariance, and structural properties of the framework, evaluate it on synthetic and molecular benchmarks, and isolate the contributions of the structural prior, the optimal-transport coupling, and the regularisation terms through controlled ablations. Flowette achieves competitive performance overall, attaining state-of-the-art results on several metrics across multiple benchmarks, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.

Reinforcement learning fine-tuning has proven effective for steering generative diffusion models toward desired properties in image and molecular domains. Graph diffusion models have similarly been applied to combinatorial structure generation, including neural architecture search (NAS). However, neural architectures are directed acyclic graphs (DAGs) where edge direction encodes functional semantics such as data flow-information that existing graph diffusion methods, designed for undirected structures, discard. We propose Directed Graph Policy Optimization (DGPO), which extends reinforcement learning fine-tuning of discrete graph diffusion models to DAGs via topological node ordering and positional encoding. Validated on NAS-Bench-101 and NAS-Bench-201, DGPO matches the benchmark optimum on all three NAS-Bench-201 tasks (91.61%, 73.49%, 46.77%). The central finding is that the model learns transferable structural priors: pretrained on only 7% of the search space, it generates near-oracle architectures after fine-tuning, within 0.32 percentage points of the full-data model and extrapolating 7.3 percentage points beyond its training ceiling. Bidirectional control experiments confirm genuine reward-driven steering, with inverse optimization reaching near random-chance accuracy (9.5%). These results demonstrate that reinforcement learning-steered discrete diffusion, once extended to handle directionality, provides a controllable generative framework for directed combinatorial structures.

There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally exist in a variety of real-life networks. Consequently, the derived limitations of GNNs, resulting from such convergence behaviour, is not truly reflective of the expressive power of GNNs when applied to realistic graphs. In this paper, we will introduce a novel method to generate random graphs that have correlated node features. The node features will be sampled in such a manner to ensure correlation between neighbouring nodes. As motivation for our choice of sampling scheme, we will appeal to properties exhibited by real-life graphs, particularly properties that are captured by the Barabási-Albert model. A theoretical analysis will strongly indicate that convergence can be avoided in some cases, which we will empirically validate on large random graphs generated using our novel method. The observed divergent behaviour provides evidence that GNNs may be more expressive than initial studies would suggest, especially on realistic graphs.

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.

Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportional to their a priori unknown value, their reward. We focus on the case where the reward has a specified, actionable structure, namely that it is submodular. We show submodularity can be harnessed to retrieve upper bounds on the reward of compositional objects that have not yet been observed. We provide in-depth analyses of the probability of such bounds occurring, as well as how many unobserved compositional objects can be covered by a bound. Following the Optimism in the Face of Uncertainty principle, we then introduce SUBo-GFN , which uses the submodular upper bounds to train a GFN. We show that SUBo-GFN generates orders of magnitude more learning signal than classical GFNs for the same number of queries to the reward function. We demonstrate the effectiveness of SUBo-GFN in terms of distribution matching and high-quality candidate generation on graph submodular tasks.

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.