The diffusion of an overdamped Brownian particle in the two-dimensional (2D
) channel bounded periodically by a parabola is studied, where the particle
is subject to an additive white or colored noise. The diffusion rate const
ant D* of the particle is evaluated by the quasi-2D approximation and the e
ffective potential approach, and the theoretical result is compared with th
e Langevin simulation. The properties of the diffusion rate constant are st
ressed for weak and strong noise cases. It is shown that, in an entropy cha
nnel, the value of D* in units of Q decreases with increasing intensity of
the colored noise. In the presence of energetic barriers, a nonmonotonic be
havior of the reduced diffusion rate constant D*Q(-1) as a function of the
noise intensity is shown.