Abstract: Climate data downscaling is the task of increasing the spatial resolution of climate data, typically by generating fine-resolution regional climate data from coarse global model output. Recent machine learning (ML) work in the related task of weather forecasting has seen significant improvements due to newly devised training methods and architectural components, but these have not yet benefited downscaling. We adapt two of these methods to create a family of lightweight probabilistic ML downscaling models built on a modified U-Net backbone and evaluate them on the CORDEX-ML-Bench suite for daily maximum temperature and precipitation across three geographic regions: the Alps, New Zealand and South Africa. We find that a two-stage training curriculum, combining deterministic pretraining with probabilistic tuning, transfers well to downscaling, beating the state-of-the-art for RMSE. Our work provides an advancement towards lightweight, probabilistic downscaling models, reducing the current trade-off between computational intensity and distributional fit.