Title: Exploring Effective Terminal State: A Null-Model-Guided Graph Diffusion Model
Primary area: learning on graphs and other geometries & topologies
Keywords: graph diffusion model, null-model, graph generation, continuous-time SDE

Abstract: Graph diffusion models have shown promise in generating complex networks, but they often suffer from two critical limitations: On the one hand, terminating the forward diffusion in pure Gaussian noise graph erases the intrinsic structural signatures of the original network, leading to sub-optimal generative outcomes. On the other hand, the unconstrained diffusion trajectory progressively obliterates topological characteristics, resulting in complete structural degradation. To address these issues, we propose Null-Model-Guided Graph Diffusion (NMG-GD), a principled framework with tailored designs for graph generation. 
First, we claim that traditional isotropic priors (e.g., Gaussian or fully structured graphs) distort salient topological features. Instead, we adopt a null-model distribution as the forward diffusion endpoint, which explicitly preserves critical network statistics such as degree sequences and clustering coefficients—ensuring global consistency. 
Second, we derive a null-model-guided continuous-time stochastic differential equation (SDE) and introduce the Position-enhanced Graph Score Network (PGSN). PGSN ingests both continuous and quantized adjacencies, fusing random-walk, shortest-path and null-model cues in a permutation-equivariant encoder,which can significantly elevates sample quality. Extensive experiments on three public datasets (including social and biological networks) demonstrate that NMG-GD achieves state-of-the-art performance. It shows the significant advantages in structural similarity and generation efficiency.

TL;DR: Null-Model-Guided Graph Diffusion replaces Gaussian noise with a null-model prior and global topological constraints, enabling more accurate and efficient graph generation.