Non-stationary Diffusion For Probabilistic Time Series Forecasting

TL;DR

This paper introduces NsDiff, a diffusion-based probabilistic forecasting framework that models non-stationary uncertainty in time series by using a Location-Scale Noise Model and an adaptive noise schedule.

Contribution

It proposes a novel diffusion model leveraging LSNM and an uncertainty-aware noise schedule to better capture time-varying uncertainty in probabilistic forecasting.

Findings

NsDiff outperforms existing methods on nine datasets.

The model effectively captures changing uncertainty patterns.

Adaptive noise scheduling improves forecast accuracy.

Abstract

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.