Very high-resolution satellite imagery from the latest generation commercial platforms provides an unprecedented capacity for imaging the Earth with very high spatial detail. However, these data are generally expensive, particularly if large areas or temporal sequences are required. In recent years, lower quality imagery has been enabled through the launch of constellations of small satellites with short revisit time. In this article, we apply for the first time a statistical approach to downscale and bias-correct these multispectral satellite data using the information contained in a limited training set of very high-resolution images. The technique, based on the direct sampling algorithm, aims at extending the coverage of high-resolution images by sampling data from a training data set, where similar lower resolution data patterns are found. Unlike the majority of the current downscaling techniques, the approach does not require colocated fine-resolution data, but it is based on the use of training images similar to the target zone. A novel specific setup is proposed, which is adaptive to different types of landscapes with no additional user effort. The results show that the proposed technique can generate more realistic images than the traditional approaches based on the parametric bias correction and bicubic interpolation. In particular, properties such as the intensity histogram, spatial correlation, and connectivity are accurately preserved. The proposed approach can be used to extend the footprint of the high-resolution images to generate new time frames or to downscale the remote sensing imagery based on a distant but structurally similar training image.