Scale-Recursive Rectified Flows for Few-Step Precipitation Ensembles

Fine-resolution precipitation estimates support flood risk assessment and water management, but coarse satellite products cannot resolve rainfall within each grid cell. Generative models address this ambiguity by producing ensembles of plausible high-resolution rainfall fields. Among these models, rectified flows generate samples by iteratively transforming random noise into rainfall fields. Reducing the number of sampling steps accelerates generation but can make ensemble members too similar, understating uncertainty. We propose a scale-recursive rectified flow that generates broad patterns before local details and guides sampling-step allocation by comparing ensemble variability with prediction error across spatial scales. Validation scores and rainfall power spectra constrain the allocation to avoid excessive amplification. In satellite-to-radar downscaling over the contiguous United States, our analysis identified broad rainfall patterns as the main source of insufficient ensemble variability under reduced sampling budgets. Allocating more steps to the coarse flow improved probabilistic accuracy and rain detection across training seeds at fixed architecture and computational cost. The proposed model also achieved better probabilistic accuracy with shorter sampling time than a nonrecursive flow using more steps.