Double-Diffusion: ODE-Prior Accelerated Diffusion Models for Spatio-Temporal Graph Forecasting

arXiv:2506.23053v2 Announce Type: replace Abstract: Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose Double-Diffusion, a denoising diffusion probabilistic model that integrates a parameter-free graph diffusion Ordinary Differential Equation (ODE) forecast as a structural prior throughout the generative process. Unlike standard diffusion approaches that generate predictions from pure noise, Double-Diffusion uses the ODE prediction as both (1) a residual learning target in the forward process via the Resfusion framework, and (2) an explicit conditioning input for the reverse denoiser, shifting the generation task from full synthesis to guided refinement. This dual integration enables accelerated sampling by initializing from an intermediate diffusion step where the ODE prior is already close to the target distribution. We further introduce the Factored Spectral Denoiser (FSD), which adopts the divided attention principle to decompose spatio-temporal-channel modeling into three efficient axes: temporal self-attention, cross-channel attention, and spectral graph convolution via the Graph Fourier Transform. Extensive experiments on four real-world sensor-network datasets spanning two domains: urban air quality (Beijing, Athens) and traffic flow (PEMS08, PEMS04, demonstrate that Double-Diffusion achieves the best probabilistic calibration (CRPS) across all datasets while scaling sublinearly in inference time, achieving a 3.8x speedup compared to standard diffusion model setup through a substantial reduction in required sampling steps.