Exact solutions of the Fokker-Planck equation are obtained for a class of non-harmonic, symmetric, attractive, 1-d potentials, and when the initial probability density is chosen "delta" peaked on the axis of symmetry of the potential. Double-well potentials are contained as special cases in our class of models. The branching time tc characterizing the transition from uni- to bimodal probability densities is obtained in limiting cases. © 1982.