This paper treats the feedback stabilization of linear diffusion systems by using a finite dimensional feedback dynamic controller. We construct a finite dimensional observer using the output functions from sensors, and the control inputs to the system are given by the feedback of the observer output. Assuming, for some fixed finite number L, that the first L modes are controllable and observable, we prove that it is possible to construct a finite dimensional feedback dynamic controller such that the diffusion system has an arbitrarily large damping constant.