Mixed-Curvature Geometric Latent Diffusion Model for Graph Generation

Existing latent graph diffusion models often learn graph representations and generative priors within a homogeneous latent geometry. This assumption is restrictive for graph generation with structural heterogeneity, where hierarchical, cyclic, locally regular, and densely connected patterns may coexist within the target distribution. Under such conditions, forcing all structural patterns into one latent geometry can introduce representation distortion, which may then propagate to generation. We propose CurvDiff, a latent graph generation framework based on mixed-curvature latent diffusion. The main idea is to model structurally different graph patterns in geometry-compatible latent factors rather than representing them in a single-curvature space. Specifically, CurvDiff learns graph embeddings in a product latent geometry consisting of hyperbolic, spherical, and Euclidean components, and maps the resulting representation to a shared tangent-space interface on which latent diffusion is defined. This provides a consistent latent pathway from representation learning to generation. To further preserve topology-relevant structure, CurvDiff uses Ricci-derived structural signals as topology-aware priors. These signals regularize latent representation learning and condition the diffusion prior, helping maintain structural consistency across representation learning and generation. Experiments on synthetic and real-world graph benchmarks show that CurvDiff achieves competitive or superior graph distribution matching compared with strong baselines, with improved fidelity on degree, clustering, and spectral statistics. These results support mixed-curvature latent diffusion as an effective approach to graph generation with structural heterogeneity.