Semantic Score Alignment for Graph Diffusion Models

Graph diffusion models have achieved promising performance in graph generation by learning reverse-time denoising processes. Existing approaches typically optimize denoising objectives on noisy node features and edge structures, where the predicted clean graphs implicitly characterize the underlying data distribution. However, conventional denoising supervision mainly focuses on individual reconstruction accuracy and does not explicitly regularize the distributional consistency between real graphs and model-predicted graphs. In this work, we propose semantic score alignment, a distribution-aware regularization framework for graph diffusion models. Motivated by the connection between denoising prediction and data distribution estimation, we introduce an additional score alignment objective to enforce consistency between real graph distributions and predicted graph distributions. Specifically, we first learn a graph-level semantic representation space that captures global structural and attribute information from graphs. The real graphs and predicted graphs are then mapped into this semantic representation space, where their density-induced score functions are estimated and aligned through Fisher divergence. This semantic score alignment provides global semantic guidance for diffusion models beyond conventional reconstruction supervision. Extensive experiments on benchmark graph generation tasks demonstrate that our proposed semantic score alignment consistently improves generation quality across diverse datasets, showing the effectiveness of distribution-level regularization for diffusion-based graph generative modeling.