We show, through simulations of a variety of one- and two-dimensional
solid-on-solid models, that nonequilibrium surface diffusion processes
in the presence of a deposition flux are generically characterized by
a nonvanishing inclination-dependent mass current along the surface.
The current stabilizes the surface, leading to Edwards-Wilkinson scali
ng for the surface fluctuations, if it is a decreasing function of inc
lination, but induces a growth instability otherwise. Both types of be
havior generally occur for the same system at different surface orient
ations.