Skull-induced aberrations remain a major drawback of transcranial ultrasound localization microscopy (ULM), degrading sensitivity and spatial accuracy through microbubble mislocalization, false detections, and imaging artifacts, such as disconnected or duplicated vessels. Here, we present a differentiable beamforming framework for automatic aberration correction in transcranial Doppler and ULM. Our approach uses spatially distributed delay-based parameterization of the aberration that is optimized in a closed-loop manner using angular coherence as an objective function. We demonstrate robust improvements of transcranial ULM, in vivo, with enhanced resolution of both mouse and nonhuman primate (NHP) brains. We also extended differentiable beamforming to functional measurements, with improvements in the sensitivity of transcranial functional ultrasound (fUS) and ULM based hemodynamic quantification. Extending this approach to 3D transcranial ULM imaging in NHPs, we show efficient correction of skull induced aberrations and removal of artifacts, such as vessel duplications. By providing a fully automated and generalizable solution for aberration correction, this work lowers a major technical barrier to transcranial ultrasound imaging, enabling broader adoption of non-invasive, super-resolution and functional neuroimaging across laboratories and across species.