Sequential models such as recurrent neural networks or transformer-based models became \textit{de facto} tools for multivariate time series forecasting in a probabilistic fashion, with applications to a wide range of datasets, such as finance, biology, medicine, etc. Despite their adeptness in capturing dependencies, assessing prediction uncertainty, and efficiency in training, challenges emerge in modeling high-dimensional complex distributions and cross-feature dependencies. To tackle these issues, recent works delve into generative modeling by employing diffusion or flow-based models. Notably, the integration of stochastic differential equations or probability flow successfully extends these methods to probabilistic time series imputation and forecasting. However, scalability issues necessitate a computational-friendly framework for large-scale generative model-based predictions. This work proposes a novel approach by blending the computational efficiency of recurrent neural networks with the high-quality probabilistic modeling of the diffusion model, which addresses challenges and advances generative models' application in time series forecasting. Our method relies on the foundation of stochastic interpolants and the extension to a broader conditional generation framework with additional control features, offering insights for future developments in this dynamic field.

本研究针对传统序列模型在高维复杂分布建模和特征间依赖性中的不足，提出了一种新的方法，将递归神经网络的计算效率与扩散模型的高质量概率建模相结合。主要发现是，这种方法能够有效推动生成模型在时间序列预测中的应用，为后续发展提供了新的思路。

递归插值用于概率时间序列预测