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.

翻译：交通预测作为时空图学习的关键应用，传统上依赖确定性模型进行精确的点估计。然而，这些模型难以识别未来观测中潜在突发波动的风险。为弥补这一不足，概率方法（尤其是扩散模型变体）应运而生，成为具有不确定性感知能力的解决方案。但现有扩散方法通常专注于为交通网络中单个传感器生成独立的未来时间序列，导致空间网络特征未充分参与概率学习过程。为更好利用交通数据中固有的空间依赖性与系统性模式，我们提出SpecSTG——一种新颖的谱扩散框架。该方法通过生成未来时间序列的傅里叶表示，将学习过程转换至富含空间信息的谱域。此外，我们的框架引入专为傅里叶输入设计的快速谱图卷积，有效缓解了现有模型的计算负担。数值实验表明，与最先进基线方法相比，SpecSTG在交通流量与交通速度数据集上均展现出卓越性能。SpecSTG的源代码可于https://anonymous.4open.science/r/SpecSTG获取。