The new results on the diffusion in dense supercritical methane reported by Ranieri et al. [Nature Communications 12, 1958 (2021)] are examined from the freezing density scaling perspective. It is demonstrated that the high pressure behaviour of the self-diffusion coefficient is consistent with the freezing density scaling of dense Lennard-Jones and hard sphere fluids. It is also observed that the Stokes–Einstein relation of the form Dη(Δ/kBT)=αSE holds in a wide pressure and density regime, where it is expected to hold (here D and η are the diffusion and shear viscosity coefficients, Δ is the intermolecular separation and kBT is the temperature). Unexpected violation occurs at highest densities in the vicinity of the freezing point, where the coefficient αSE reaches values ≃10% higher than the upper theoretically expected limit.