Parameter regionalization for ungauged basins is an important and difficult topic in hydrology. The challenge becomes even more pronounced when seeking for flexible transfer operators that link physical descriptors to spatially distributed parameters of a conceptual model and impose spatial constraints needed, given sparse observation data. This work presents the Hybrid Data Assimilation Parameter Regionalization (HDA-PR) approach employing accurate adjoint-based cost gradients to learn complex transfer operators designed for high-resolution hydrological models. The core idea of HDA-PR lies in incorporating inferable regionalization mappings, such as multivariate regressions or neural networks, into a differentiable hydrological model and its variational data assimilation process. This integration enables the exploitation of the valuable information contained in heterogeneous datasets across extensive spatio-temporal computational domains, especially when dealing with high-dimensional regionalization problems. HDA-PR is thoroughly tested at multiple resolutions over several basin sets with contrasted sizes and characteristics, using worldwide and regional databases. The results showcase high discharge modeling performances in calibration and in spatio-temporal validation at pseudo-ungauged sites. The parametric stability and information extraction from databases are analyzed. Finally, a bidirectional LSTM network is trained on top of the regionalized hydrological model to predict modeling errors at multiple temporal scales. All methods are implemented in the open source SMASH package, and the regionalization method can be adapted for state-parameter correction from multi-source data, at multiple time scales such as for operational data assimilation. Furthermore, it can be applied to other differentiable geophysical models.