We present the results of a simple numerical model with phenomenological cloud growth and explosive disruption processes, and with fountain-launched ballistic motions of disrupted cloud fragments out of the disk. These processes generate an effective scattering of gas elements over much larger distances than noncircular impulses in the plane, which are quickly damped. The result is the evolution of the global cloud density profile to an exponential form on a roughly Gyr timescale. This is consistent with our previous results on the effects of star scattering off massive clumps in young disks, and gas holes in dwarf galaxies. However, in those cases the scattering processes generated thick, warm/hot stellar disks. Here we find that the exponential gas disks remain cold. Star formation in this gas would produce a thin exponential stellar disk.