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The paper describes diffusion of particles in a tilted spatially periodic potential under the action of external forces in the case of a low friction. It is shown that in underdamped systems, a region of temperature-abnormal diffusivity (TAD) exists, in which the diffusion coefficient increases with decreasing temperature. The TAD width and its position depend on the friction coefficient and the system parameters. The analytical expression for diffusion coefficients in TAD area is derived. These results are important for experimental investigations of TAD and its application.