The paper identifies a limitation of discrete graph diffusion models: independent edge updates combined with exchangeability force the terminal prior to be an Erdős–Rényi graph, which hampers denoising and leads to loss of node heterogeneity. To overcome this, the authors propose a Latent Sociability Prior (LSP) and a joint diffusion process that co‑evolves latent sociability variables with graph structure, eliminating edge independence while maintaining exchangeability. Experiments on several graph generation datasets show that this approach better captures graph distributions than baseline methods that lack node features.
arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.
arXiv:2603. 08825v2 Announce Type: replace-cross Abstract: 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.
The paper introduces PG‑DiGress, a constraint‑guided discrete denoising diffusion model that generates power‑grid feeder topologies while respecting electrical compatibility and radiality rules. By injecting feeder constraints as soft masks during the reverse diffusion process and applying a final projection step, the model learns categorical node and edge patterns from existing feeder data. Evaluation shows a dramatic improvement in rule compliance, raising the strict feeder pass rate from 13.7% to 96.8%, and the generated graphs can be converted into executable feeder models for downstream analysis.
Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem.
The paper introduces simplex denoising, a generative framework that operates on the probability simplex rather than directly in the discrete state space. It employs a non‑Markovian noising scheme where noisy representations at different times are conditionally independent, preserving theoretical guarantees while removing unnecessary constraints. Empirical results show that unrestrained simplex denoising outperforms strong discrete diffusion and flow‑matching baselines on both synthetic and real‑world graph benchmarks.
arXiv:2609.39739v1 Announce Type: new Abstract: Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures...
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.
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
arXiv:2505. 03649v4 Announce Type: replace-cross Abstract: Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields.
The paper investigates discrete graph diffusion models (GDMs) and demonstrates that they can memorize training data when conditioned on corrupted training graphs. By analyzing reverse diffusion trajectories on two‑block stochastic block models, the authors find that the model almost perfectly reconstructs the corrupted training graph, a phenomenon they call conditional memorization. This memorization coincides with a growing generalization gap and precedes the emergence of community structure in generated graphs, occurring across all tested node sizes.
The paper introduces xVGAE, a hierarchical variational graph autoencoder designed for exchangeable graphs. Leveraging the Aldous-Hoover theorem, the model uses a graph-level latent variable, exchangeable node-specific latent variables, and a graphon function to learn and generate graph distributions efficiently. Experiments demonstrate that xVGAE produces high-quality graphs quickly while capturing key structural properties of the training data.