Motivated by recent experimental and theoretical results, we have studied the diffraction of atoms (D, 3He, 4He) from KCl(001). To perform this study, we have computed continuos potential energy surfaces (PESs) using density functional theory to obtain total interaction energies, with and without taking into account van der Waals forces, and the corrugation reduction procedure. Subsequently, we have performed quantum dynamics simulations using the multi-configuration time-dependent Hartree method. Our simulated spectra compare rather well with those recorded experimentally, specially well for 3He. The agreement is, in general, better for incidence along the [100] direction. In the case of He projectiles, the inclusion of vdW forces does not systematically improve agreement with the experiment. Finally, in agreement with similar calculations for other systems, we have found that the diffraction spectra are quite sensitive to the subtle characteristics of PES, whereas phonons and electronic excitations seem to play a minor role.