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

TL;DR

SpecSTG introduces a fast probabilistic spatio-temporal traffic forecasting framework by performing diffusion in the graph Fourier domain, thereby leveraging spatial structure more effectively than time-domain approaches. The method replaces spatial convolutions with a light-weight spectral convolution and uses a spectral recurrent encoder together with a spectral WaveNet denoiser, enabling autoregressive sampling with substantially reduced computation. Empirical results on PEMS04/PEMS08 show consistent improvements in point forecasts (up to 8% RMSE gain) and modest gains in uncertainty calibration (up to 0.78% CRPS), while achieving around 3.33x faster training/validation relative to the best baselines. The approach offers a practical, scalable route to uncertainty-aware traffic forecasting, with robust performance across varying hyperparameters and data variations.

Abstract

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.

Figures (8)

• Figure 1: Illustrations: (a) an example of traffic STG; (b) traffic flow forecasting in future 60 minutes with GMAN (deterministic) and SpecSTG (probabilistic) on PEMS04.
• Figure 2: The overview of SpecSTG. Illustrations of TimeGrad and GCRDD are provided to show the novelty and advantage of our approach.
• Figure 3: The denoising network $\bm{\epsilon}_{\bm{\theta}}$ is a modified WaveNet structure.
• Figure 4: Forecasting visualizations of TimeGrad (green), GCRDD (blue), and SpecSTG (red). (a) and (b) are results on speed data (PEMS04S), while (c) presents results on flow data (PEMS04F).
• Figure 5: Time efficiency of training, validation, and sampling.

Theorems & Definitions (1)

• Remark 1: Complexity Analysis