High spatio-temporal resolution near-surface projected data is vital for climate change impact studies and adaptation. We derived the highest statistically downscaled resolution multivariate ensemble currently available: daily 1 km until the end of the century. Deep learning models were employed to develop transfer functions for precipitation, water vapor pressure, radiation, wind speed, and, maximum, mean and minimum temperature. Perfect prognosis is the particular statistical downscaling methodology applied, using a subset of the ReKIS data set for Saxony as predictands, the ERA5 reanalysis as during-training predictors and the CORDEX-EUR11 ensemble as projected predictors. The performance of the transfer functions was validated with the VALUE framework, yielding highly satisfactory results. Particular attention was given to the three major perfect prognosis assumptions, for which several tests were carried out and thoroughly discussed. From the latter, we corroborated their fulfillment to a high degree, thus, the derived projections are considered adequate and relevant for impact modelers. In total, 18 runs for RCP85, 1 for RCP45, and 4 for RCP26 were downscaled under both stochastic and deterministic approaches. This multivariate ensemble could drive more accurate and diverse impact studies in the region. Generally, the projected climatologies are in agreement with coarser resolution projections. Nevertheless, statistical particularities were observed for some projections, thus, a list of caveats for potential users is given. Due to the scalability of the presented methodology, further possible applications with additional datasets are proposed. Lastly, several potential improvement prospects are discussed toward the ideal subsequent iteration of the perfect prognosis statistical downscaling methodology.