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.

Current prediction models treat uncertainty as constant, but real-world uncertainty fluctuates dramatically, making these predictions unreliable precisely when we need them most.We developed NsDiff, the first diffusion-based framework that learns how uncertainty changes over time. Unlike standard models, it automatically adjusts its predictions by analyzing patterns in historical data. Our key innovation enables the prediction distribution to dynamically adapt to forecasted features.In experiments across critical applications, from weather forecasting to patient hospitalization estimates, NsDiff consistently provided more accurate and robust uncertainty estimates than existing models, demonstrating wide potential for real-world applications.