Bäcklund transformations for diffusion equations

A class of Bäcklund transformations is deduced for the diffusion equation (S(u))_t = (C(u,u_x))_x by taking advantage of the conservative form of the equation. The transformations are used for obtaining new relations connecting various equations of the type u_t = (u^au_x)_x and u_t = u^au_xx.