# Auto-Regressive Moving Diffusion Models for Time Series Forecasting

arXiv: https://arxiv.org/abs/2412.09328 · HTML: https://mlsanity.com/paper/2412.09328/

## Key facts

- Cited by 10 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 16 of its 40 references that are in the map.
- First posted on arXiv 12 Dec 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, 16 of 16)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Can ChatGPT Forecast Stock Price Movements? Return Predictability and Large Language Models](https://mlsanity.com/paper/2304.07619/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process](https://mlsanity.com/paper/2403.05751/) (2024)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Client: Cross-variable Linear Integrated Enhanced Transformer for Multivariate Long-Term Time Series Forecasting](https://mlsanity.com/paper/2305.18838/) (2023)
- [Latent Knowledge-Guided Video Diffusion for Scientific Phenomena Generation from a Single Initial Frame](https://mlsanity.com/paper/2411.11343/) (2024)
- [Survey and Taxonomy: The Role of Data-Centric AI in Transformer-Based Time Series Forecasting](https://mlsanity.com/paper/2407.19784/) (2024)
- [CLeaRForecast: Contrastive Learning of High-Purity Representations for Time Series Forecasting](https://mlsanity.com/paper/2312.05758/) (2023)
- [Cross-variable Linear Integrated ENhanced Transformer for Photovoltaic power forecasting](https://mlsanity.com/paper/2406.03808/) (2024)

## Built on by (most cited first, 10 of 10)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Latent Generative Solvers for Generalizable Long-Term Physics Simulation](https://mlsanity.com/paper/2602.11229/) (2026)
- [ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion](https://mlsanity.com/paper/2609.37078/) (2026)
- [Pattern-Guided Diffusion Models](https://mlsanity.com/paper/2512.13945/) (2025)
- [Sparse Compositional Flow Matching by geometric assembly from motion primitives](https://mlsanity.com/paper/2605.23341/) (2026)
- [ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.02117/) (2026)
- [Deterministic Prediction as Global Velocity: Flow Matching for Probabilistic Time-Series Forecast](https://mlsanity.com/paper/2610.18621/) (2026)

## Abstract (arXiv)

Time series forecasting (TSF) is essential in various domains, and recent advancements in diffusion-based TSF models have shown considerable promise. However, these models typically adopt traditional diffusion patterns, treating TSF as a noise-based conditional generation task. This approach neglects the inherent continuous sequential nature of time series, leading to a fundamental misalignment between diffusion mechanisms and the TSF objective, thereby severely impairing performance. To bridge this misalignment, and inspired by the classic Auto-Regressive Moving Average (ARMA) theory, which views time series as continuous sequential progressions evolving from previous data points, we propose a novel Auto-Regressive Moving Diffusion (ARMD) model to first achieve the continuous sequential diffusion-based TSF. Unlike previous methods that start from white Gaussian noise, our model employs chain-based diffusion with priors, accurately modeling the evolution of time series and leveraging intermediate state information to improve forecasting accuracy and stability. Specifically, our approach reinterprets the diffusion process by considering future series as the initial state and historical series as the final state, with intermediate series generated using a sliding-based technique during the forward process. This design aligns the diffusion model's sampling procedure with the forecasting objective, resulting in an unconditional, continuous sequential diffusion TSF model. Extensive experiments conducted on seven widely used datasets demonstrate that our model achieves state-of-the-art performance, significantly outperforming existing diffusion-based TSF models. Our code is available on GitHub: https://github.com/daxin007/ARMD.