  We consider the driven diffusion of Brownian particles in 1D periodic
potentials using the recently proposed Stochastic Path Integral Hyperdynamics
(SPHD) scheme [L.Y. Chen and L.J.M. Horing, J. Chem. Phys. {\bf 126}, 224103
(2007)]. First, we consider the case where a single Brownian particle is moving
in a spatially periodic potential and subjected to an external ac driving
force. We confirm that there is no stochastic resonance in this system and find
that at higher frequencies the diffusion coefficient $D$ is strongly
suppressed. The second case is that of a dimer moving in a periodic potential
with a static bias. For this case, there's a strong suppression of $D$ when the
dimer bond length is an integer multiple of the lattice constant of the
potential. For both cases, we demonstrate how the SPHD allows us to extract the
dynamical information exactly at different bias levels from a single simulation
run, by calculating the corresponding statistical re-weighting factors.
