In physical foaming processes of thermoplastics, a liquid mixture consisting of a molten polymer with a dissolved blowing agent is extruded through a die or injected into a mold. The morphology of the foam matrix strongly depends on the mutual diffusion coefficient D11 of the liquid polymer-blowing agent mixture. For a better understanding of the underlying physical mechanisms during the foaming process and the development of corresponding models, accurate knowledge of D11 is needed. This work reports on the simultaneous measurement of D11 and the thermal diffusivity a of liquid mixtures consisting of polystyrene melts with dissolved nitrogen (N2) or carbon dioxide (CO2) at mass fractions wsolute up to 0.003 or 0.02 and temperatures T between (433 and 533) K using dynamic light scattering (DLS). The determined D11 range is between (1 and 4) × 109 m2⋅s−1 and are slightly larger for the mixtures containing N2 at a given T and wsolute. D11 could be determined with an average expanded relative uncertainty of 18%. Considering all investigated state points and the achieved experimental uncertainties, both D11 and a are independent on the amount of dissolved gas, despite relatively large mole fractions of the dissolved blowing agents xsolute of 0.997 and 0.93.