Rapid adsorbate diffusion into the solid is known to suppress the desorption yield measured in a thermal desorption experiment. We show that this suppression can be controlled (at least partly) by pulsed-laser heating at rates in excess of 10(10) K/s. As an example, we analyze the D/Zr system. In this case, deuterium adsorbed on a surface rapidly diffuses into the bulk of Zr with increasing temperature, and the deuterium desorption probability measured with conventional heating rates (beta less than or equal to 100 K/s) is as low as approximate to 10(-4) for polycrystalline Zr foils (deuterium desorption is not observed at all from single-crystal Zr from which dissolved H/D has been removed). Heating the Zr(0001) surface by pulsed-laser thermal excitation with beta similar or equal to 10(11) K/s is demonstrated to result in the increase of the deuterium desorption probability up to approximately 0.01. To interpret this observation, general equations for describing associative desorption accompanied by adsorbate diffusion into the solid are simplified by employing the specifics of the temperature-programmed kinetic regimes with a linear increase of temperature. The desorption yield calculated without any adjustable parameters is in good agreement with the experimental results.