This paper considers diffusion processes {Xε(t)} on R2, which are perturbations of dynamical system {X(t)} (dX(t) = b(X(t))dt) on R2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {Xε(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.