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

2026-03-03 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

StaTS is a novel diffusion model designed for probabilistic time series forecasting, addressing limitations of fixed noise schedules in existing models. It introduces a Spectral Trajectory Scheduler (STS) that learns a data-adaptive noise schedule, regularized by spectral objectives to enhance structural preservation and stepwise invertibility. Complementing this, the Frequency Guided Denoiser (FGD) estimates schedule-induced spectral distortion and uses it to modulate denoising strength, enabling heterogeneous restoration across diffusion steps and variables. The model employs a two-stage training procedure to stabilize the coupling between schedule learning and denoiser optimization. Experiments on eight real-world multivariate time series benchmarks, including Electricity, ILI, and Traffic, demonstrate that StaTS consistently outperforms state-of-the-art baselines in CRPS and MAE, while maintaining strong performance with fewer sampling steps and lower computational costs.

Key takeaway

For research scientists developing diffusion models for time series forecasting, you should consider implementing data-adaptive noise schedules with spectral regularization. This approach, as demonstrated by StaTS, significantly improves probabilistic forecasting quality and point accuracy, especially under limited inference budgets. Focusing on frequency-guided denoising can also lead to more robust and efficient models, reducing reliance on manual schedule tuning and enhancing the fidelity of uncertainty quantification.

Key insights

Adaptive noise scheduling and frequency-guided denoising significantly improve probabilistic time series forecasting accuracy and uncertainty.

Principles

• Data-adaptive noise schedules improve structural preservation.
• Spectral regularization enhances stepwise invertibility.
• Frequency-domain guidance modulates denoising strength.

Method

StaTS learns noise schedules and denoisers through alternating updates, using spectral regularization for the schedule and frequency-guided modulation for denoising, stabilized by a two-stage training process.

In practice

• Optimize noise schedules for specific datasets.
• Incorporate frequency-domain analysis for denoising.
• Use two-stage training for stable coupled optimization.

Topics

• Diffusion Models
• Time Series Forecasting
• Adaptive Noise Schedules
• Spectral Regularization
• Frequency Guided Denoising

Code references

• zjt-gpu/StaTS
• zhouhaoyi/ETDataset

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.