Probabilistic End-to-End Hierarchical Forecasting with Conditional Flow Matching

Probabilistic forecasting in hierarchical settings requires generating distributions over future trajectories that satisfy strict aggregation constraints while capturing complex uncertainty. We propose Hierarchical Conditional Flow Matching (HCFM), an end-to-end framework in which future trajectories are generated by integrating a continuous-time dynamical system that combines a learnable residual flow with explicit terms for past consistency and hierarchical coherence. The framework supports two complementary instantiations: projected dynamics that preserve sample-wise coherence throughout integration, and soft-guided dynamics with exact endpoint reconciliation. In both cases, HCFM produces individually coherent forecast samples without committing to a fixed parametric output family. Across six public benchmarks, a single configuration (HCFM-UNet) attains the lowest overall scaled Continuous Ranked Probability Score (sCRPS) on five, with an average relative reduction of 14% against the strongest baseline (CLOVER), with competitive point-forecast accuracy.