The study of time series is crucial for understanding trends and anomalies over time, enabling predictive insights across various sectors. Spatio-temporal data, on the other hand, is vital for analyzing phenomena in both space and time, providing a dynamic perspective on complex system interactions. Recently, diffusion models have seen widespread application in time series and spatio-temporal data mining. Not only do they enhance the generative and inferential capabilities for sequential and temporal data, but they also extend to other downstream tasks. In this survey, we comprehensively and thoroughly review the use of diffusion models in time series and spatio-temporal data, categorizing them by model category, task type, data modality, and practical application domain. In detail, we categorize diffusion models into unconditioned and conditioned types and discuss time series and spatio-temporal data separately. Unconditioned models, which operate unsupervised, are subdivided into probability-based and score-based models, serving predictive and generative tasks such as forecasting, anomaly detection, classification, and imputation. Conditioned models, on the other hand, utilize extra information to enhance performance and are similarly divided for both predictive and generative tasks. Our survey extensively covers their application in various fields, including healthcare, recommendation, climate, energy, audio, and transportation, providing a foundational understanding of how these models analyze and generate data. Through this structured overview, we aim to provide researchers and practitioners with a comprehensive understanding of diffusion models for time series and spatio-temporal data analysis, aiming to direct future innovations and applications by addressing traditional challenges and exploring innovative solutions within the diffusion model framework.

翻译：时间序列研究对于理解随时间变化的趋势与异常至关重要，能够为各领域提供预测性洞见。另一方面，时空数据对于分析现象在空间与时间维度上的演变具有关键意义，为复杂系统相互作用提供动态视角。近年来，扩散模型在时间序列与时空数据挖掘中得到广泛应用。它们不仅增强了序列与时序数据的生成与推断能力，还延伸至其他下游任务。本综述全面而深入地回顾了扩散模型在时间序列与时空数据中的应用，依据模型类别、任务类型、数据模态及实际应用领域进行分类梳理。具体而言，我们将扩散模型划分为无条件与有条件两类，并分别讨论时间序列与时空数据场景。无条件模型以无监督方式运行，可细分为基于概率与基于分数的模型，服务于预测、异常检测、分类与填补等预测性与生成性任务。有条件模型则利用额外信息提升性能，并同样按预测性与生成性任务进行划分。本综述广泛涵盖这些模型在医疗健康、推荐系统、气候、能源、音频及交通等领域的应用，为理解模型如何分析与生成数据提供基础认知。通过这一结构化概述，我们旨在为研究人员与实践者提供关于时间序列与时空数据分析中扩散模型的全面理解，以期通过应对传统挑战并探索扩散模型框架内的创新解决方案，引领未来的技术创新与应用发展。