City-Wide Origin-Destination Matrix Generation via Cascaded Graph Denoising Diffusion

The Origin-destination (OD) matrix provides an estimation of population mobility flow between regions, which is the backbone of modern spatial data systems, enabling critical tasks like urban simulation, traffic analysis and resource scheduling. However, expanding these systems to new cities is often hindered by data scarcity, lacking of historical mobility logs due to privacy or cost constraints. This calls for computational models to act as generative operators within spatial data pipelines, synthesizing dynamic mobility behaviors from static urban space. Existing works typically treat matrix entries as independent variables, overlooking the global relational structure of the flows. Consequently, these methods inevitably lose critical topological consistencies, resulting in synthetic data that lacks inherent network properties (e.g., sparsity and scaling behaviors), severely limiting its utility for complex spatial queries and analysis. Our research introduces a novel approach that views the OD matrix generation from a network perspective, utilizing the graph diffusion model to learn the joint probability distribution of matrix elements (edge weights) condition on regional city characteristics (node features). To overcome the difficulty of modeling city-wide OD matrix covering thousands of regions with millions of potential flows, our method employs a cascaded schema, initially constructing the network topology to pinpoint non-zero elements, i.e., OD flows. This design acts as a sparsity-aware filter, restricting the computationally expensive flow generation to only valid edges. This drastically improves the modeling efficiency, ensuring the scalability for large-scale, sparse spatial databases. To thoroughly reproduce important network properties contained in city-wide OD matrices, we design an elaborated graph denoising network integrating a node property augmentation module based on the graph transformer. Empirical experiments on three large US cities have verified that our method can generate OD matrices for new cities with network statistics remarkably similar to the ground truth, further achieving superior performance over competitive baselines in terms of the realism.