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.

翻译：时间序列预测（TSF）在各个领域都至关重要，而基于扩散的TSF模型的最新进展已显示出相当大的潜力。然而，这些模型通常采用传统的扩散模式，将TSF视为基于噪声的条件生成任务。这种方法忽略了时间序列固有的连续序列特性，导致扩散机制与TSF目标之间存在根本性的错位，从而严重损害了性能。为了弥合这种错位，并受到经典的自回归移动平均（ARMA）理论的启发——该理论将时间序列视为从先前数据点演进而来的连续序列进程，我们提出了一种新颖的自回归移动扩散（ARMD）模型，首次实现了基于连续序列扩散的TSF。与以往从高斯白噪声开始的方法不同，我们的模型采用基于链式扩散的先验，精确建模时间序列的演化，并利用中间状态信息来提高预测的准确性和稳定性。具体而言，我们的方法通过将未来序列视为初始状态、历史序列视为最终状态来重新解释扩散过程，并在前向过程中使用基于滑动的技术生成中间序列。这一设计使扩散模型的采样过程与预测目标保持一致，从而形成了一个无条件的、连续序列扩散的TSF模型。在七个广泛使用的数据集上进行的大量实验表明，我们的模型实现了最先进的性能，显著优于现有的基于扩散的TSF模型。我们的代码可在GitHub上获取：https://github.com/daxin007/ARMD。