# Diffusion Models for Time Series Applications: A Survey

arXiv: https://arxiv.org/abs/2305.00624 · HTML: https://mlsanity.com/paper/2305.00624/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 51 of its 64 references that are in the map.
- First posted on arXiv 1 May 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Flexible Diffusion Modeling of Long Videos](https://mlsanity.com/paper/2205.11495/) (2022)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)

## Built on by (most cited first, 30 of 72)

- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [Gradient-Free Generation for Hard-Constrained Systems](https://mlsanity.com/paper/2412.01786/) (2024)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Attacks and Defenses for Generative Diffusion Models: A Comprehensive Survey](https://mlsanity.com/paper/2408.03400/) (2024)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Empowering Time Series Analysis with Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2405.02358/) (2024)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modeling](https://mlsanity.com/paper/2503.02445/) (2025)
- [A Survey of Generative Techniques for Spatial-Temporal Data Mining](https://mlsanity.com/paper/2405.09592/) (2024)
- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [DiffsFormer: A Diffusion Transformer on Stock Factor Augmentation](https://mlsanity.com/paper/2402.06656/) (2024)
- [Vision-Enhanced Time Series Forecasting via Latent Diffusion Models](https://mlsanity.com/paper/2502.14887/) (2025)
- [A Comprehensive Survey on Generative Diffusion Models for Structured Data](https://mlsanity.com/paper/2306.04139/) (2023)
- [Diffusion Methods for Generating Transition Paths](https://mlsanity.com/paper/2309.10276/) (2023)
- [Navigating Tabular Data Synthesis Research: Understanding User Needs and Tool Capabilities](https://mlsanity.com/paper/2405.20959/) (2024)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [Boosting Data Analytics With Synthetic Volume Expansion](https://mlsanity.com/paper/2310.17848/) (2023)
- [Vision-Language Synthetic Data Enhances Echocardiography Downstream Tasks](https://mlsanity.com/paper/2403.19880/) (2024)
- [Diverse Intra- and Inter-Domain Activity Style Fusion for Cross-Person Generalization in Activity Recognition](https://mlsanity.com/paper/2406.04609/) (2024)
- [A Financial Time Series Denoiser Based on Diffusion Model](https://mlsanity.com/paper/2409.02138/) (2024)
- [Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Survey](https://mlsanity.com/paper/2409.18214/) (2024)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [The Alpha-Alternator: Dynamic Adaptation To Varying Noise Levels In Sequences Using The Vendi Score For Improved Robustness and Performance](https://mlsanity.com/paper/2502.04593/) (2025)

## Abstract (arXiv)

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.