Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability arising from their inherent stochasticity. In this paper, we revisit time series diffusion models and present a comprehensive framework that encompasses most existing diffusion-based methods. Building on this theoretical foundation, we propose a novel diffusion-based time series forecasting model, the Series-to-Series Diffusion Bridge Model ($\mathrm{S^2DBM}$), which leverages the Brownian Bridge process to reduce randomness in reverse estimations and improves accuracy by incorporating informative priors and conditions derived from historical time series data. Experimental results demonstrate that $\mathrm{S^2DBM}$ delivers superior performance in point-to-point forecasting and competes effectively with other diffusion-based models in probabilistic forecasting.

本研究解决了时间序列预测中扩散模型的随机性导致可预测性不稳定的问题。作者提出了一种新颖的扩散基础时间序列预测模型——系列到系列扩散桥模型（$\mathrm{S^2DBM}$），利用布朗桥过程降低反向估计中的随机性，并结合历史时间序列数据的有用先验和条件，提高了预测精度。实验结果表明，$\mathrm{S^2DBM}$在点对点预测中表现优越，并在概率预测中与其他扩散模型有效竞争。

系列到系列的扩散桥模型