The polaron formation due to the strong interaction of electrons with the optical phonons in a layered manganese oxides is considered. The diffusion of nearly localized polarons in the presence of the spin-dependent and multiple scattering on the randomly oriented and/or distributed magnetic moments of atoms is considered. The spin diffusion coefficient in the case of the exchange interaction between the diffusive but nearly localized polarons is evaluated. It is shown that the polaron localization leads to the vanishing of the spin diffusion and hence the ferromagnetic phase transition. The spin-polaron effect caused by the interaction of polarons with the spin fluctuations further significantly reduces conductivity near the temperature of the ferromagnetic phase transition as shown.