GD-Mamba: Adaptive Cross-Domain Alternating Graph Diffusion Model with Selective State Space Model

Graph generation is a critical task in deep learning, aimed at learning and modelling the structural distribution of graphs, with broad applications in areas such as social network analysis and molecular design. Current mainstream graph generation methods adopt diffusion models as the foundational architecture. Graph data typically consists of two modalities: the discrete graph modality based on topological structures, and the continuous latent space modality based on vector representations. Diffusion models for the graph modality focus on denoising discrete nodes and edges and lack unified control over the global structure, resulting in jump-like changes in the generation process. In contrast, diffusion models for the latent space modality perform denoising in a continuous space, resulting in gradual changes throughout the generation process. To incorporate global semantic guidance from the latent space modality into graph modality denoising, while injecting discrete priors from the graph modality into latent space denoising, we propose GD-Mamba, an Adaptive Cross-Domain Alternating Graph Diffusion Model with Selective State Space Model. GD-Mamba alternately performs denoising between the continuous and discrete modalities, namely the graph and latent space modalities. To stabilize the dual-modality generation process, a two-level Mamba structure (G-Mamba and S-Mamba) is designed to align features across both modalities. Additionally, a multiscale wavelet positional encoding attention (MSW-PE) mechanism is introduced in the cross-domain mapping between both modalities. This mechanism effectively extracts the core structure of graphs by locating neighbourhoods of nodes and edges at different frequency scales, improving the accuracy and robustness in the alternating denoising process. The experimental results demonstrate that the proposed GD-Mamba method has superior performance on both generic graph datasets and molecular graph datasets.