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

arXiv: https://arxiv.org/abs/2603.00037 · HTML: https://mlsanity.com/paper/2603.00037/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Accelerating Diffusion Sampling with Optimized Time Steps](https://mlsanity.com/paper/2402.17376/) (2024)
- [Schedule On the Fly: Diffusion Time Prediction for Faster and Better Image Generation](https://mlsanity.com/paper/2412.01243/) (2024)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [Score-Optimal Diffusion Schedules](https://mlsanity.com/paper/2412.07877/) (2024)
- [Improving Time Series Forecasting via Instance-aware Post-hoc Revision](https://mlsanity.com/paper/2505.23583/) (2025)
- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [ANT: Adaptive Noise Schedule for Time Series Diffusion Models](https://mlsanity.com/paper/2410.14488/) (2024)
- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [Conditional Denoising Meets Polynomial Modeling: A Flexible Decoupled Framework for Time Series Forecasting](https://mlsanity.com/paper/2410.13253/) (2024)
- [MuLan: Adapting Multilingual Diffusion Models for Hundreds of Languages with Negligible Cost](https://mlsanity.com/paper/2412.01271/) (2024)
- [Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matching](https://mlsanity.com/paper/2511.14488/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond Augmentation: Score-Guided Pathological Prior for EEG-based Depression Detection](https://mlsanity.com/paper/2606.00180/) (2026)

## Abstract (arXiv)

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/.