  A solvable model is proposed and analyzed to reveal the mechanism underlying
the diffusion enhancement recently reported for a model of molecular motors and
predicted to be observed in the biological rotary motor $\rm F_1$-ATPase. It
turns out that the diffusion enhancement for the present model can
approximately described by a random walk in which the waiting time for a step
to occur is exponentially distributed and it takes nonzero time to proceed
forward by the step. It is shown that the diffusion coefficient of such a
random walk can significantly be increased when the average waiting time is
comparable to the average stepping time.
