A quantum theory of thermal desorption of light noble gases, at low temperatures, in the framework of the distorted-wave Born approximation, is presented. Such a theory has been applied to the calculation of the angle-resolved thermal desorption flux, and time-of-flight spectrum for Ne-Cu(111) using a microscopic description of the phonons of Cu(111), and a realistic gas-solid potential. We show that desorption is driven by long-wavelength phonons, but the precise angular dependence results from the temperature-dependent interplay of statistical and dynamical factors. The angular distribution is narrower than cosine at 4 K, broader than cosine at 12 K, and distinctly non-cosine for temperatures greater than 20 K with the maximum away from the surface normal. He desorbing from graphite shows similar features.