The temperature dependence of the diffusivity of delocalized positronium atom scattered on longitudinal acoustic photons in alkali halide crystals has been investigated theoretically. The detailed calculations including the non-elastic scattering at low temperature and the influence of the positronium scattering form-factor have been performed within the relaxation time approximation. The diffusion of self-trapped positronium is analyzed qualitatively. The results obtained are in good agreement with known experimental data.