Comments on the Algebraic Properties of Dilaton Actions

We study the relation between the dilaton action and sigma models for the Goldstone bosons of the spontaneous breaking of the conformal group. We argue that the relation requires that the sigma model is diffeomorphism invariant. The origin of the WZW terms for the dilaton is clarified and it is shown that in this approach the dilaton WZW term is necessarily accompanied by a Weyl invariant term proposed before from holographic considerations.