SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting

Traffic forecasting, a crucial application of spatio-temporal graph (STG) learning, has traditionally relied on deterministic models for accurate point estimations. Yet, these models fall short of identifying latent risks of unexpected volatility in future observations. To address this gap, probabilistic methods, especially variants of diffusion models, have emerged as uncertainty-aware solutions. However, existing diffusion methods typically focus on generating separate future time series for individual sensors in the traffic network, resulting in insufficient involvement of spatial network characteristics in the probabilistic learning process. To better leverage spatial dependencies and systematic patterns inherent in traffic data, we propose SpecSTG, a novel spectral diffusion framework. Our method generates the Fourier representation of future time series, transforming the learning process into the spectral domain enriched with spatial information. Additionally, our approach incorporates a fast spectral graph convolution designed for Fourier input, alleviating the computational burden associated with existing models. Numerical experiments show that SpecSTG achieves outstanding performance with traffic flow and traffic speed datasets compared to state-of-the-art baselines. The source code for SpecSTG is available at https://anonymous.4open.science/r/SpecSTG.