摘要： 时间序列预测在金融、气象、交通等领域具有广泛应用，尤其在多分辨率预测场景中，不同粒度的预测需求日益凸显。传统的确定性模型难以刻画未来序列的不确定性，而现有生成式模型如变分自编码器等则在生成质量与建模灵活性方面存在一定局限。为此，提出一种面向多分辨率时间序列预测的协变量条件扩散模型（MrC²DM）。该模型以历史时间序列与未来协变量作为条件输入，通过引入分辨率类别嵌入控制预测粒度，并利用扩散生成机制从噪声中逐步还原未来序列，从而实现对未来动态的不确定性建模与高质量预测。实验结果表明，MrC²DM在七个公开数据集上平均较最优确定性模型分别提升5.4%的MAE和13.5%的MSE性能，较最优生成式模型在CRPS指标上提升28.1%，同时在跨分辨率预测任务中保持更高的稳定性与泛化能力。

Abstract: Time series forecasting has been widely applied in fields such as finance, meteorology, and transportation. In multi-resolution forecasting scenarios, the demand for predictions at different temporal granularities is increasingly prominent. Traditional deterministic models struggle to capture the uncertainty of future sequences, while existing generative models, such as variational autoencoders, often suffer from limitations in generation quality and modeling flexibility. To address these challenges, we propose a Covariate-Conditioned Diffusion Model for Multi-Resolution Time Series Forecasting (MrC²DM). The model takes historical time series and future covariates as conditional inputs, introduces a resolution-category embedding to control prediction granularity, and employs a diffusion-based generative mechanism to progressively denoise and reconstruct future sequences from noise, thereby enabling uncertainty modeling and high-quality forecasting of future dynamics. Experimental results show that MrC²DM outperforms the best deterministic baselines by 5.4% (MAE) and 13.5% (MSE), and surpasses the best generative models by 28.1% (CRPS) across seven public datasets. Moreover, MrC²DM maintains higher stability and generalization ability in cross-resolution forecasting tasks.