StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser

TL;DR

StaTS is proposed, a diffusion model for probabilistic time series forecasting that learns the noise schedule and the denoiser through alternating updates and stabilizes the coupling between schedule learning and denoiser optimization.

Abstract

Diffusion models have been used for probabilistic time series forecasting and show strong potential. However, fixed noise schedules often produce intermediate states that are hard to invert and a terminal state that deviates from the near noise assumption. Meanwhile, prior methods rely on time domain conditioning and seldom model schedule induced spectral degradation, which limits structure recovery across noise levels. We propose StaTS, a diffusion model for probabilistic time series forecasting that learns the noise schedule and the denoiser through alternating updates. StaTS includes Spectral Trajectory Scheduler (STS) that learns a data adaptive noise schedule with spectral regularization to improve structural preservation and stepwise invertibility, and Frequency Guided Denoiser (FGD) that estimates schedule induced spectral distortion and uses it to modulate denoising strength for heterogeneous restoration across diffusion steps and variables. A two stage training procedure stabilizes the coupling between schedule learning and denoiser optimization. Experiments on multiple real world benchmarks show consistent gains, while maintaining strong performance with fewer sampling steps. Our code is available at https://github.com/zjt-gpu/StaTS/.

Figures (14)

• Figure 1: Conventional diffusion relies on fixed schedule, whereas our approach learns a data adaptive schedule, yielding more distinguishable intermediate states and better controlled terminal noise.
• Figure 2: Overview of StaTS. The Spectral Trajectory Scheduler (STS) learns an adaptive variance schedule $\beta(t)$ to govern forward corruption and regularize the spectral flatness trajectory over diffusion time. The FGD includes a conditional guidance module for encoding the history and a frequency denoising module for frequency-aware denoising under noise corruption. StaTS is trained in two stages: we alternately update STS and FGD for $k$ epochs, then freeze STS and train FGD to convergence with the learned schedule.
• Figure 3: Visualize results on the ETTh1 dataset.
• Figure 4: Visualize results on Electricity dataset.
• Figure 5: Normalized spectral evolution of the forward corruption and reverse denoising trajectories under different diffusion steps.

Theorems & Definitions (4)

• Theorem 3.1
• Theorem 3.2
• proof
• proof