Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In this work, we propose Conditionally Whitened Generative Models (CW-Gen), a framework that incorporates prior information through conditional whitening. Theoretically, we establish sufficient conditions under which replacing the traditional terminal distribution of diffusion models, namely the standard multivariate normal, with a multivariate normal distribution parameterized by estimators of the conditional mean and covariance improves sample quality. Guided by this analysis, we design a novel Joint Mean-Covariance Estimator (JMCE) that simultaneously learns the conditional mean and sliding-window covariance. Building on JMCE, we introduce Conditionally Whitened Diffusion Models (CW-Diff) and extend them to Conditionally Whitened Flow Matching (CW-Flow). Experiments on five real-world datasets with six state-of-the-art generative models demonstrate that CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches. Empirical results further demonstrate that CW-Gen can effectively mitigate the effects of distribution shift.

翻译：多元时间序列的概率预测面临非平稳性、变量间依赖关系及分布偏移等挑战。尽管近期扩散模型与流匹配模型展现出潜力，但它们常忽略条件均值与协方差等具有信息量的先验。本研究提出条件白化生成模型（CW-Gen），该框架通过条件白化机制融合先验信息。理论上，我们建立了充分条件，证明将扩散模型传统的终端分布（标准多元正态分布）替换为由条件均值与协方差估计量参数化的多元正态分布可提升样本质量。基于此分析，我们设计了一种新颖的联合均值-协方差估计器（JMCE），能够同步学习条件均值与滑动窗口协方差。以JMCE为基础，我们提出了条件白化扩散模型（CW-Diff）并将其扩展至条件白化流匹配（CW-Flow）。在五个真实世界数据集上对六种前沿生成模型的实验表明，CW-Gen能持续提升预测性能，相较于无先验方法能更有效地捕捉非平稳动态与变量间相关性。实证结果进一步证明CW-Gen可有效缓解分布偏移的影响。