  Giant diffusion, where the diffusion coefficient of a Brownian particle in a
periodic potential with an external force is significantly enhanced by the
external force, is a non-trivial non-equilibrium phenomenon. We propose a
simple stochastic model of giant diffusion, which is based on a biased
continuous-time random walk (CTRW). In this model, we introduce a flight time
in the biased CTRW. We derive the diffusion coefficients of this model by the
renewal theory and find that there is a maximum diffusion coefficient when the
bias is changed. Giant diffusion is universally observed in the sense that
there is a peak of the diffusion coefficient for any tilted periodic potentials
and the degree of the diffusivity is greatly enhanced especially for
low-temperature regimes. The biased CTRW models with flight times are applied
to diffusion under three tilted periodic potentials. Furthermore, the
temperature dependence of the maximum diffusion coefficient and the external
force that attains the maximum are presented for diffusion under a tilted
sawtooth potential.
