A Survey on Diffusion Models for Time Series and Spatio-Temporal Data

TL;DR

This survey analyzes diffusion models applied to time series and spatio-temporal data, organizing the literature into unconditional and conditional families and across predictive and generative tasks. It details standard (DDPM/Score SDE) and advanced (conditional, latent, and other variants) models, with a focus on denoisers and their architectural biases for temporal data. The paper surveys a broad range of applications from healthcare and traffic to climate, energy, audio, and finance, and discusses practical challenges such as efficiency and robustness, offering directions toward multimodal fusion and foundation-model–driven temporal reasoning. By providing a structured taxonomy, task- and data-centric perspectives, the authors lay groundwork for future diffusion-model-based data mining in time series and spatio-temporal domains.

Abstract

Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate, energy, audio, and traffic. By separating applications for time series and spatio-temporal data, we offer a structured perspective on model category, task type, data modality, and practical application domain. This study aims to provide a solid foundation for researchers and practitioners, inspiring future innovations that tackle traditional challenges and foster novel solutions in diffusion model-based data mining tasks and applications. For more detailed information, we have open-sourced a repository at https://github.com/yyysjz1997/Awesome-TimeSeries-SpatioTemporal-Diffusion-Model.

Figures (7)

• Figure 1: Trends in the cumulative number of papers related to diffusion models for time series and spatio-temporal data.
• Figure 2: An overview of diffusion models for time series and spatio-temporal data analysis. In the diffusion process, $x_k$ and $x_{k-1}$ denote the results after adding noise at step $k$ and $k-1$, respectively. This process can be represented by the size of the controlling steps $\beta_{k} \in (0,1)$, the identity matrix $\mathbf{I}$, and a Gaussian distribution $\mathcal{N}(x;\mu,\sigma)$ of $x$ with the mean $\mu$ and the covariance $\sigma$. During the denoising process, the model attempts to iteratively learn the data distribution by modelling the distribution ${p}_\theta(x_{k-1}|x_k)$. The functions $\mu_\theta(\cdot)$ and variance $\sigma_\theta(\cdot)$ are the model learnable parameters.
• Figure 3: Representative diffusion models for time series and spatio-temporal data in recent years.
• Figure 4: Illustrations of time series and spatio-temporal data.
• Figure 5: Different types of generative models.