Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting
Yanfeng Yang, Siwei Chen, Pingping Hu, Zhaotong Shen, Yingjie Zhang, Zhuoran Sun, Shuai Li, Ziqi Chen, Kenji Fukumizu
TL;DR
This work addresses probabilistic forecasting for multivariate time series under non-stationarity and distribution shift by introducing Conditionally Whitened Generative Models (CW-Gen). CW-Gen combines a Joint Mean–Covariance Estimator (JMCE) with conditional whitening to create CW-Diff and CW-Flow, enabling priors based on the conditional mean and sliding-window covariance to guide diffusion and flow generation. The authors derive a sufficient KL-divergence bound showing when a learned conditional Gaussian terminal distribution improves sample quality, and they implement JMCE to produce these priors with PSD covariance control. Empirically, CW-Gen improves probabilistic and, in many cases, point forecasting performance across five real-world datasets and six baselines, while mitigating distribution shift; the framework is extensible to other diffusion/flow models and supports end-to-end training. Overall, CW-Gen provides a principled, modular approach to integrate informative priors into generative time-series models for more accurate and robust forecasting.
Abstract
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.