  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.
