We show that a continuous local semiflow of Ck-maps on a finite- dimensional Ck-manifoldM can be embedded into a local Ck-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [2]. We prove that finite-dimensional realizations for interest rate models are highly regular objects, namely given by submanifolds M of D(A∞), where A is the generator of a strongly continuous semigroup