Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. In recent years, the concept of diffusion has been extended to time series applications, and many powerful models have been developed. Considering the deficiency of a methodical summary and discourse on these models, we provide this survey as an elementary resource for new researchers in this area and also an inspiration to motivate future research. For better understanding, we include an introduction about the basics of diffusion models. Except for this, we primarily focus on diffusion-based methods for time series forecasting, imputation, and generation, and present them respectively in three individual sections. We also compare different methods for the same application and highlight their connections if applicable. Lastly, we conclude the common limitation of diffusion-based methods and highlight potential future research directions.

翻译：扩散模型作为基于深度学习的生成模型家族，在前沿机器学习研究中日益凸显其重要性。凭借生成与观测数据高度相似样本的卓越性能，扩散模型现广泛应用于图像、视频和文本合成领域。近年来，扩散概念已拓展至时间序列应用领域，并催生了众多强大模型。鉴于当前缺乏针对此类模型的系统性总结与论述，本文综述旨在为该领域新研究者提供基础资源，同时激发未来研究灵感。为便于理解，我们首先简要介绍扩散模型的基本原理。在此基础上，重点阐述基于扩散方法的时间序列预测、插补和生成三大应用方向，并分别以独立章节进行详述。我们亦对相同应用场景下的不同方法进行对比，并尽可能揭示其内在联系。最后，我们总结了扩散方法存在的共性局限，并展望了潜在的研究方向。