Land surface soil moisture (SSM) has important roles in the energy balance of the land surface and in the water cycle. Downscaling of coarse-resolution SSM remote sensing products is an efficient way for producing fine-resolution data. However, the downscaling methods used most widely require full-coverage visible/infrared satellite data as ancillary information. These methods are restricted to cloud-free days, making them unsuitable for continuous monitoring. The purpose of this study is to overcome this limitation to obtain temporally continuous fine-resolution SSM estimations. The local spatial heterogeneities of SSM and multiscale ancillary variables were considered in the downscaling process both to solve the problem of the strong variability of SSM and to benefit from the fusion of ancillary information. The generation of continuous downscaled remote sensing data was achieved via two principal steps. For cloud-free days, a stepwise hybrid geostatistical downscaling approach, based on geographically weighted area-to-area regression kriging (GWATARK), was employed by combining multiscale ancillary variables with passive microwave remote sensing data. Then, the GWATARK-estimated SSM and China Soil Moisture Dataset from Microwave Data Assimilation SSM data were combined to estimate fine-resolution data for cloudy days. The developed methodology was validated by application to the 25-km resolution daily AMSR-E SSM product to produce continuous SSM estimations at 1-km resolution over the Tibetan Plateau. In comparison with ground-based observations, the downscaled estimations showed correlation (R ≥ 0.7) for both ascending and descending overpasses. The analysis indicated the high potential of the proposed approach for producing a temporally continuous SSM product at fine spatial resolution.