The diffusion of trace gases in snow and firn is a crucial process for snow-atmosphere interactions and air mixing in firn. It is very sensitive to interactions of the trace gas with the ice surface. We developed an experimental setup to measure the effective diffusion constant of nitrogen oxides (NO_x = NO + NO₂) and the highly soluble nitrous acid (HONO). The method combines X-ray microtomography and a radioactive tracer technique: tomography provides the microscopic configuration of the pore space as well as the amount of ice surface accessible for the gas, while radioactively labeled molecules reveal the dynamics of diffusion. Bringing together the precise characterization of snow microstructure and the dynamics of tracer diffusion, the partitioning between gas phase and ice can be studied. We present results measured in two different snow types, fresh snow and aged, rounded snow. The fast diffusion of NO and NO₂ was measured by analyzing the temporal evolution of their gas phase concentration downstream of the snow samples. The effective diffusivity of HONO could be directly measured from the steady state migration profiles of radioactively labeled HO¹³NO molecules. The measured effective diffusion constants of NO and NO₂ agree well with the theory of diffusion in porous media. This underlines that tomography may be used to map diffusivity in snow or firn with high spatial resolution. Owing to the interactions of HONO with ice, the effective diffusion constant of HONO was 2 to 3 orders of magnitude smaller than the diffusivity in air.