Abstract. The rivers of High-mountain Asia provide freshwater to around 1.9 billion people. However, precipitation, the main driver of river flow, is still poorly understood due to limited in situ measurements in this area. Existing tools to interpolate these measurements or downscale and bias-correct precipitation models have several limitations. To overcome these challenges, this paper uses a probabilistic machine learning approach called multi-fidelity Gaussian processes (MFGPs) to downscale the fifth ECMWF climate reanalysis (ERA5). The method is first validated by downscaling ERA5 precipitation data over data-rich Europe and then data-sparse upper Beas and Sutlej river basins in the Himalayas. We find that MFGPs are simpler to implement and more applicable to smaller datasets than other state-of-the-art machine learning methods. MFGPs are also able to quantify and narrow the uncertainty associated with the precipitation estimates, which is especially needed over ungauged areas and can be used to estimate the likelihood of extreme events that lead to floods or droughts. Over the upper Beas and Sutlej river basins, the precipitation estimates from the MFGP model are similar to or more accurate than available gridded precipitation products (APHRODITE, TRMM, CRU TS, and bias-corrected WRF). The MFGP model and APHRODITE annual mean precipitation estimates generally agree with each other for this region, with the MFGP model predicting slightly higher average precipitation and variance. However, more significant spatial deviations between the MFGP model and APHRODITE over this region appear during the summer monsoon. The MFGP model also presents a more effective resolution, generating more structure at finer spatial scales than ERA5 and APHRODITE. MFGP precipitation estimates for the upper Beas and Sutlej basins between 1980 and 2012 at a 0.0625° resolution (approx. 7 km) are jointly published with this paper.