CoFlow: Leaf-Space Factorization for Point and Probabilistic Forecast Reconciliation

Forecast reconciliation is usually posed as a point-adjustment problem. When forecasts must also quantify uncertainty, coherence must extend to the joint predictive law, while its center may not optimize the target point-forecast loss. We introduce CoFlow, a post-hoc leaf-space framework that separates a coherent anchor, a joint error law, and a separately optimized point forecast. Mapping both error draws and point corrections through the summing matrix guarantees coherence while allowing predictive shape and point accuracy to be selected independently. This factorization also exposes aggregate dispersion as a central calibration problem. For Gaussian node errors with any predictive-to-true variance ratio, we theoretically derive exact expressions for coverage and expected CRPS and interval-score regret, together with quadratic lower bounds. Under attenuated cross-leaf covariance, these penalties increase with the share of aggregate variance carried by dependence. CoFlow combines Gaussian, copula, count, empirical, and flow-based leaf laws with coherent attention-based and sparse constraint-routing point heads. Across 29 hierarchies, three rolling origins, and five seeds, Tweedie with routing improves relative MAE by 9.8%, nCRPS by 6.2%, and normalized interval score by 16.0% over MinT. An RBIG-Gaussian mixture improves nCRPS on all 29 datasets and both nMIS and coverage gap on 28. Ablations isolate gains from dependence, marginal shape, and point estimation.