The point spread function (PSF) is an important measure of spatial resolution in CCDs for point-like objects, since it can affect use in imaging and spectroscopic applications. We present new data and theoretical developments in the study of lateral charge diffusion in thick, fully-depleted charge-coupled devices (CCDs) developed at Lawrence Berkeley National Laboratory (LBNL). Because they are fully depleted, the LBNL devices have no field-free region, and diffusion can be controlled through the application of an external bias voltage. We give results for a 3512x3512 format, 10.5 ?m pixel back-illuminated p-channel CCD developed for the SuperNova/ Acceleration Probe (SNAP), a proposed satellite-based experiment designed to study dark energy. The PSF was measured at substrate bias voltages between 3 V and 115 V. At a bias voltage of 115V, we measure an rms diffusion of 3.7 +- 0.2 ?m. Lateral charge diffusion in LBNL CCDs is thus expected to meet the SNAP requirements.