Earth is unique within our solar system in having a convective regime dominated by plate tectonic processes. More typical of rocky, 'terrestrial' planets is a "stagnant lid" regime, where the entire lithosphere is a single plate, variably punctured by plume-driven volcanic activity.As such, a signficant fraction of 'Earth-like' exoplanets might instead have stagnant lids. For hot stagnant lid planets like Venus, high temperatures towards the base of the lid mean that solid-state diffusion potentially provides a mechanism for redistributing lighter, faster-diffusing volatile elements such as H. To investigate the importance of this mechanism a 1-d model is used to constrain volatile flux from a realtively undegassed planetry interior into a hot stagnant lid. Diffusion only results in signficant flux of H through an oxidised lid; diffusion of H in reduced stagnant lids and diffusion of other volatile elements, is inconsequential. For modelled Venusian tempearture profiles H diffusion fronts progress a limited distance (10s of km) into the lid over Gyr timescales. However, for a small relative increase in lid temperature (i.e. a slightly hotter than Venus exoplanet), H diffusion into the lid becomes considerable over shorter timescales. H flux upwards into the lid eventually stagnates with decreasing temperature. However, H flux markedly reduces mantle solidus in lower portions of the lid, decreasing lid stability and promoting lid rejuvination. Given the inlfuence of H on a range of mantle properties from melt relations to rheology, future models of stagnant lid planetary evolution should assess the role of diffusion in redistributing H.