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The activation energy for desorption (Edes) and that for surface diffusion (Esd) of adsorbed molecules on dust grains are two of the most important parameters for the chemistry in the interstellar medium. Although Edes is often measured by laboratory experiments, the measurement of Esd is sparse. Due to the lack of data, astrochemical models usually assume a simple scaling relation, Esd = fEdes, where f is a constant, irrespective of adsorbed species. Here, we experimentally measure Esd for CH4, H2S, OCS, CH3OH, and CH3CN on water-ice surfaces using an ultra-high-vacuum transmission electron microscope (UHV-TEM). Compiling the measured Esd values and Edes values from the literature, we find that the value of f ranges from ~0.2 to ~0.7, depending on the species. Unless f (or Esd) for the majority of species is available, a natural alternative approach for astrochemical models is running multiple simulations, varying f for each species randomly. In this approach, ranges of molecular abundances predicted by multiple simulations, rather than abundances predicted by each simulation, are important. We here run 10,000 simulations of astrochemical models of molecular clouds and protostellar envelopes, randomly assigning a value of f for each species. In the former case, we identify several key species whose Esd most strongly affects the uncertainties of the model predictions; Esd for those species should be investigated in future laboratory and quantum chemical studies. In the latter case, uncertainties in the Esd of many species contribute to the uncertainties in the model predictions.