  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 quantifying future uncertainties.
Recently, many probabilistic methods, especially variants of diffusion models,
have been proposed to fill this gap. However, existing diffusion methods
typically deal with individual sensors separately when generating future time
series, resulting in limited usage of spatial information in the probabilistic
learning process. In this work, we propose SpecSTG, a novel spectral diffusion
framework, to better leverage spatial dependencies and systematic patterns
inherent in traffic data. More specifically, 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.
Compared with state-of-the-arts, SpecSTG achieves up to 8% improvements on
point estimations and up to 0.78% improvements on quantifying future
uncertainties. Furthermore, SpecSTG's training and validation speed is 3.33X of
the most efficient existing diffusion method for STG forecasting. The source
code for SpecSTG is available at https://anonymous.4open.science/r/SpecSTG.
