DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment
Abstract
Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimizing the conditional negative log-likelihood, typically estimated by the mean squared error. However, this estimation proves biased when the label sequence exhibits autocorrelation. In this paper, we propose DistDF, which achieves alignment by minimizing a distributional discrepancy between the conditional distributions of forecast and label sequences. Since such conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. The proposed discrepancy is tractable, differentiable, and readily compatible with gradient-based optimization. Extensive experiments show that DistDF improves diverse forecasting models and achieves leading performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.
Cite
@article{arxiv.2510.24574,
title = {DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment},
author = {Hao Wang and Licheng Pan and Yuan Lu and Zhixuan Chu and Xiaoxi Li and Shuting He and Zhichao Chen and Haoxuan Li and Qingsong Wen and Zhouchen Lin},
journal= {arXiv preprint arXiv:2510.24574},
year = {2026}
}