Statistical downscaling is commonly used in climate modeling to obtain high-resolution spatial projections of future climate scenarios from the coarse-resolution outputs projected by global climate models. Unfortunately, most of the statistical downscaling approaches using standard regression methods tend to emphasize projecting the conditional mean of the data while paying scant attention to the extreme values that are rare in occurrence yet critical for climate impact assessment and adaptation studies. This paper presents a statistical downscaling framework that focuses on the accurate projection of future extreme values by estimating directly the conditional quantiles of the response variable. We also extend the proposed framework to a semi-supervised learning setting and demonstrate its efficacy in terms of inferring the magnitude, frequency, and timing of climate extreme events. The proposed approach outperformed baseline statistical down-scaling approaches in 85% of the 37 stations evaluated, in terms of the magnitude projected for extreme data points.