The point spread function (PSF) is ubiquitous in remote sensing. This paper investigated the effect of the PSF on the downscaling of continua. Geostatistical approaches were adopted to incorporate explicitly, and reduce the influence of, the PSF effect in downscaling. Two general cases were considered: univariate and multivariate. In the univariate case, the input coarse spatial resolution image is the only image available for downscaling. Area-to-point kriging was demonstrated to be a suitable solution in this case. For the multivariate case, a finer spatial resolution image (or images) observed under different conditions (e.g., at a different wavelength) is available as auxiliary data for downscaling. Area-to-point regression kriging was shown to be a suitable solution for this case. Moreover, a new solution was developed for estimating the PSF in image scale transformation. The experiments show that the PSF effect influences downscaling greatly and that downscaling can be enhanced obviously by considering the PSF effect through the geostatistical approaches and the PSF estimation solution proposed.