Diffusion of slow, neutrons in an extended uniform medium is treated by a method which accounts for the thermal motion of the medium. If neutron capture is absent, a single integral equation has to be solved, in order to determine the velocity distribution and the diffusion coefficient. A system of such equations is obtained for a capturing medium. For the case of a non-capturing monoatomic gaseous medium several approximations are discussed, which express the diffusion coefficient as a function of the atomic weight.