A Non-isotropic Time Series Diffusion Model with Moving Average Transitions

Chenxi Wang, Linxiao Yang, Zhixian Wang, Liang Sun, Yi Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:65144-65166, 2025.

Abstract

Diffusion models, known for their generative ability, have recently been adapted to time series analysis. Most pioneering works rely on the standard isotropic diffusion, treating each time step and the entire frequency spectrum identically. However, it may not be suitable for time series, which often have more informative low-frequency components. We empirically found that direct application of standard diffusion to time series may cause gradient contradiction during training, due to the rapid decrease of low-frequency information in the diffusion process. To this end, we proposed a novel time series diffusion model, MA-TSD, which utilizes the moving average, a natural low-frequency filter, as the forward transition. Its backward process is accelerable like DDIM and can be further considered a time series super-resolution. Our experiments on various datasets demonstrated MA-TSD’s superior performance in time series forecasting and super-resolution tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25dy, title = {A Non-isotropic Time Series Diffusion Model with Moving Average Transitions}, author = {Wang, Chenxi and Yang, Linxiao and Wang, Zhixian and Sun, Liang and Wang, Yi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {65144--65166}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wang25dy/wang25dy.pdf}, url = {https://proceedings.mlr.press/v267/wang25dy.html}, abstract = {Diffusion models, known for their generative ability, have recently been adapted to time series analysis. Most pioneering works rely on the standard isotropic diffusion, treating each time step and the entire frequency spectrum identically. However, it may not be suitable for time series, which often have more informative low-frequency components. We empirically found that direct application of standard diffusion to time series may cause gradient contradiction during training, due to the rapid decrease of low-frequency information in the diffusion process. To this end, we proposed a novel time series diffusion model, MA-TSD, which utilizes the moving average, a natural low-frequency filter, as the forward transition. Its backward process is accelerable like DDIM and can be further considered a time series super-resolution. Our experiments on various datasets demonstrated MA-TSD’s superior performance in time series forecasting and super-resolution tasks.} }
Endnote
%0 Conference Paper %T A Non-isotropic Time Series Diffusion Model with Moving Average Transitions %A Chenxi Wang %A Linxiao Yang %A Zhixian Wang %A Liang Sun %A Yi Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wang25dy %I PMLR %P 65144--65166 %U https://proceedings.mlr.press/v267/wang25dy.html %V 267 %X Diffusion models, known for their generative ability, have recently been adapted to time series analysis. Most pioneering works rely on the standard isotropic diffusion, treating each time step and the entire frequency spectrum identically. However, it may not be suitable for time series, which often have more informative low-frequency components. We empirically found that direct application of standard diffusion to time series may cause gradient contradiction during training, due to the rapid decrease of low-frequency information in the diffusion process. To this end, we proposed a novel time series diffusion model, MA-TSD, which utilizes the moving average, a natural low-frequency filter, as the forward transition. Its backward process is accelerable like DDIM and can be further considered a time series super-resolution. Our experiments on various datasets demonstrated MA-TSD’s superior performance in time series forecasting and super-resolution tasks.
APA
Wang, C., Yang, L., Wang, Z., Sun, L. & Wang, Y.. (2025). A Non-isotropic Time Series Diffusion Model with Moving Average Transitions. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:65144-65166 Available from https://proceedings.mlr.press/v267/wang25dy.html.

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