# The Rise of Diffusion Models in Time-Series Forecasting

arXiv: https://arxiv.org/abs/2401.03006 · HTML: https://mlsanity.com/paper/2401.03006/

## Key facts

- Cited by 25 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 60 of its 104 references that are in the map.
- First posted on arXiv 5 Jan 2024.

## 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 60)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)

## Built on by (most cited first, 25 of 25)

- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting](https://mlsanity.com/paper/2410.03229/) (2024)
- [VisionTS++: Cross-Modal Time Series Foundation Model with Continual Pre-trained Vision Backbones](https://mlsanity.com/paper/2508.04379/) (2025)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [Auto-Regressive Moving Diffusion Models for Time Series Forecasting](https://mlsanity.com/paper/2412.09328/) (2024)
- [Probabilistic Forecasting via Autoregressive Flow Matching](https://mlsanity.com/paper/2503.10375/) (2025)
- [Constrained Posterior Sampling: Time Series Generation with Hard Constraints](https://mlsanity.com/paper/2410.12652/) (2024)
- [Byte Pair Encoding for Efficient Time Series Forecasting](https://mlsanity.com/paper/2505.14411/) (2025)
- [Conditional Lagrangian Wasserstein Flow for Time Series Imputation](https://mlsanity.com/paper/2410.07550/) (2024)
- [RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.02341/) (2025)
- [High-Performance Self-Supervised Learning by Joint Training of Flow Matching](https://mlsanity.com/paper/2512.19729/) (2025)
- [How to Unlock Time Series Editing? Diffusion-Driven Approach with Multi-Grained Control](https://mlsanity.com/paper/2506.05276/) (2025)
- [DeXposure-FM: A Time-series, Graph Foundation Model for Credit Exposures and Stability on Decentralized Financial Networks](https://mlsanity.com/paper/2602.03981/) (2026)
- [Hallucination Detection and Mitigation with Diffusion in Multi-Variate Time-Series Foundation Models](https://mlsanity.com/paper/2508.00881/) (2025)
- [STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems](https://mlsanity.com/paper/2508.19011/) (2025)
- [Conditional Deep Levy Models for Exotic Derivatives: History-Aware Path Generation and P-Q Payoff Diagnostics](https://mlsanity.com/paper/2509.13374/) (2025)
- [CSI Prediction Using Diffusion Models](https://mlsanity.com/paper/2510.11214/) (2025)
- [It Takes Two to Tango: Two Parallel Samplers Improve Quality in Diffusion Models for Limited Steps](https://mlsanity.com/paper/2510.21802/) (2025)
- [Structured Noise Modeling for Enhanced Time-Series Forecasting](https://mlsanity.com/paper/2511.19657/) (2025)
- [EMFusion: Uncertainty-Aware Conditional Diffusion Model for Multivariate Narrow-band Exposure Forecasting](https://mlsanity.com/paper/2512.15067/) (2025)
- [Graph2TS: Structure-Controlled Time Series Generation via Quantile-Graph VAEs](https://mlsanity.com/paper/2603.19970/) (2026)
- [Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching](https://mlsanity.com/paper/2604.11178/) (2026)
- [Conditional Diffusion Models for Energy-Efficient Driving](https://mlsanity.com/paper/2608.28142/) (2026)
- [Diffusion models for eye-gaze trajectory generation using position and velocity representations](https://mlsanity.com/paper/2609.05522/) (2026)
- [ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.01320/) (2026)

## Abstract (arXiv)

This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information on diffusion models, detailing their conditioning methods and reviewing their use in time-series forecasting. The analysis covers 11 specific time-series implementations, the intuition and theory behind them, the effectiveness on different datasets, and a comparison among each other. Key contributions of this work are the thorough exploration of diffusion models' applications in time-series forecasting and a chronologically ordered overview of these models. Additionally, the paper offers an insightful discussion on the current state-of-the-art in this domain and outlines potential future research directions. This serves as a valuable resource for researchers in AI and time-series analysis, offering a clear view of the latest advancements and future potential of diffusion models.