Atmospheric forcing data suffer from inherent biases and errors, which further add up when fed into hydrological models generating biased simulations of fluxes like streamflow and evapotranspiration (ET). One of the ways to minimize this effect is data fusion using deep learning networks like long short-term memory (LSTM), which can implicitly correct or fuse datasets, but interpreting their complex networks to understand individual biases is difficult. Here, we propose a novel approach utilizing a differentiable hydrological model, which produces static or time-dynamic weights associated with different datasets. For the current work, we focused on three precipitation datasets: Daymet, Maurer, and NLDAS2. These weights could serve as a medium for data fusion of multiple datasets or become a set of time-dynamic ‘correction factors’ to adjust inherent biases when using only one dataset. Notably, the first scheme of data fusion enabled our differentiable hydrologic model to almost reach the performance of LSTM, and in addition, improvements were seen in high and low flow performance metrics while maintaining prediction performance for ET. This suggests overall improvement in the hydrological structure of the model. When fusing multiple datasets, the trained weights showed almost equal importance for Daymet and NLDAS2 while the Maurer dataset showed the least importance. In the another experiment, when we trained on a single dataset, these weights acted as ‘correction factors’ and resulted in adjusted-NLDAS2 having increased similarity to Daymet in terms of patterns and trends. We conclude by providing a new approach to fuse datasets and correct biases in a manner suitable for climate studies.