Non-stationary Diffusion For Probabilistic Time Series Forecasting
This work addresses the challenge of modeling time-varying uncertainty in time series forecasting, which is crucial for applications like finance and weather prediction, representing an incremental improvement over existing diffusion models.
The paper tackles the problem of probabilistic time series forecasting by addressing the non-stationary nature of uncertainty, which existing diffusion models fail to capture due to constant variance assumptions; it introduces Non-stationary Diffusion (NsDiff) based on a Location-Scale Noise Model, achieving superior performance on nine real-world and synthetic datasets.
Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.