时间序列预测想同时要准均值和好分布？TORF用两阶段把这两件事拆开做，不用采样就能保住均值，短长期都跑赢了现有方法。
TORF框架将均值预测与不确定性估计解耦，第一阶段用预训练确定性模型生成准确均值，第二阶段用严格奇函数的受限归一化流学习残差分布，无需采样即可保证均值保持。实验表明TORF在短长期预测中同时达到最优确定性精度（NMAE）和强密度估计性能（CRPS）。该方法解决了传统参数方法在联合NLL训练下点精度下降和生成模型采样成本高的问题。
Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.