Skillful medium-range precipitation forecasting at kilometer scale remains challenging over complex terrain because precipitation arises from multiscale nonlinear processes that global models cannot explicitly resolve at affordable cost. Global AI weather models can produce skillful medium-range forecasts, but their native 0.25 degrees resolution limits direct use for local hazard applications. Statistical downscaling can help bridge this gap, yet existing approaches often struggle with state-dependent, and especially lead-time-dependent, biases in global forecasts. We introduce SwAIther-Precip, a lead-time-aware downscaling framework that converts coarse-resolution AIFS forecasts into probabilistic km-scale precipitation fields over Switzerland. First, a U-Net conditioned on lead time via feature-wise linear modulation deterministically corrects systematic biases at coarse resolution. This targeted correction enables a cheaper super-resolution stage conditioned only on corrected precipitation, allowing direct training on observations rather than on the full atmospheric state. A diffusion-based model then generates fine-scale spatial variability independently of lead time. Using AIFS forecasts and CombiPrecip radar-gauge observations, SwAIther-Precip reduces CRPS by 48% relative to raw AIFS. The generated fields reproduce observed spatial variability with spectral fidelity above 0.85 at large scales and 0.88 at small scales, corresponding to an effective resolution of approximately 4 km on a 1 km grid for lead times up to 5 days. Training across lead times further improves long-range performance, yielding a 13% CRPS reduction at 6 days relative to lead-time-specific models. These results show that explicitly correcting lead-time-dependent biases before generative super-resolution is key to efficient km-scale probabilistic downscaling of global AI precipitation forecasts.

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