Expressions for diffusion constants in molten salts have been obtained in terms of the inter-ionic pair potentials and the pair distribution functions. Numerical attempts for diffusion constants in molten alkali halides are carried out and results agreed fairly with those obtained by molecular-dynamics simulation and with some experimental data. Based on the coupling of generalized Langevin equation and damped Einstein oscillator equation, ions' velocity autocorrelation functions have also been described and are numerically applied for molten potassium fluoride. The deviation from the Nernst-Einstein relation was also discussed in detail. In Appendixes A x B x C, the short-time expansion of velocity correlation functions in relation to the partial conductivities and the diffusion constants were obtained up to the term of t(4) and these were compared with a model function described by the form of cos(omegat)sech(ttau).