Super-resolution ultrasound microvessel imaging based on ultrasound localization microscopy (ULM) is an emerging imaging modality that is capable of resolving micron scaled vessels deep into tissue. In practice, ULM is limited by the need for contrast injection, long data acquisition, and computationally expensive post-processing times. In this study, we present a contrast-free super-resolution Doppler (CS Doppler) technique that uses deep generative networks to achieve super-resolution with short data acquisition. The training dataset is comprised of spatiotemporal ultrafast ultrasound signals acquired from in vivo mouse brains, while the testing dataset includes in vivo mouse brain, chicken embryo chorioallantoic membrane (CAM), and healthy human subjects. The in vivo mouse imaging studies demonstrate that CS Doppler could achieve an approximate 2-fold improvement in spatial resolution when compared with conventional power Doppler. In addition, the microvascular images generated by CS Doppler showed good agreement with the corresponding ULM images as indicated by a structural similarity index of 0.7837 and a peak signal-to-noise ratio of 25.52. Moreover, CS Doppler was able to preserve the temporal profile of the blood flow (e.g., pulsatility) that is similar to conventional power Doppler. Finally, the generalizability of CS Doppler was demonstrated on testing data of different tissues using different imaging settings. The fast inference time of the proposed deep generative network also allows CS Doppler to be implemented for real-time imaging. These features of CS Doppler offer a practical, fast, and robust microvascular imaging solution for many preclinical and clinical applications of Doppler ultrasound.