Depending on the device structure and hence the electric field present within a CCD, there is often a considerable time for charge clouds generated within the silicon to diffuse and spread outward before being collected at the buried channel. This charge spreading has an important effect on the spatial and energy resolution of CCDs used for soft x-ray, optical, and high energy particle imaging. Further theory on this is presented with regard to the performance of CCDs currently under development, to broaden their spectral response while minimizing the thickness of the field-free region below the depletion layer. It is shown that the charge cloud profiles resulting from field-free diffusion have broad wings that can lead to significant charge splitting between adjacent pixels, even for field-free region thicknesses ~1 um. Formulas are also presented for diffusion in the field region and the substrate.