A new model which explains the deviation from Arrhenius law of the diffusion coefficient of hydrogen in amorphous metals is proposed. The model is based on the short-order range of the structure and its temperature dependence. The model is applied to simulate the diffusion behavior of hydrogen in dilute amorphous Fe-H alloy. Results show that accounting for the temperature dependence of the structure of the alloy leads to pronounced temperature dependence of the activation energy for diffusion processes. This effect reflects itself in the non-Arrhenius behavior of the diffusivity of small-atomic-volume impurities in amorphous metals.