The GRACE and GRACE-FO satellite missions provide mass variations as a fundamentally new observation type for a broad spectrum of novel applications in Earth science disciplines, including oceanography, geophysics, hydrology, and hydrometeorology. Despite all the key findings in hydrology, the utility of GRACE-derived Terrestrial Water Storage Anomaly (TWSA) and its time derivative Terrestrial Water Storage Flux (TWSF) have mainly been limited to large catchments due to their coarse spatial resolution. Here, we propose a method to downscale TWSF by incorporating available finer-resolution data. We determine the downscaled TWSF and its uncertainty within a proposed Bayesian framework by incorporating the fine-scale data of TWSF and Soil Moisture Change (SMC) from different available sources. For the Bayesian ingredients, we rely on GRACE data to obtain the prior and rely on copula models to obtain nonparametric likelihood functions based on the statistical relationship between GRACE TWSF with fine-scale TWSF data and SMC. We apply our method to the Amazon Basin and assess the performances of our products from various fine-scale input datasets of TWSFs and SMCs. Given the lack of ground truth for TWSF, we validate our results against space-based Surface Water Storage Change (SWSC) in the Amazon river system and also against the Vertical Crustal Displacements Rate (VCDR) observed by the Global Positioning System (GPS). Overall, the results show that the proposed method is able to estimate a downscaled TWSF, which is informed by GRACE and fine-scale data. Validation shows that our downscaled products are better anticorrelated with VCDR (−0.81) than fine-scale TWSF (−0.73) and show a mean relative RMSE of 26% with SWSC versus 70% for fine-scale TWSF. The proposed methodology can be extended to other coarse scale datasets, which are crucial for hydrological application at regional and local scales.