  We present a class of diffraction-free partially coherent beams each member
of which is comprised of a finite power, non-accelerating Airy bump residing on
a statistically homogeneous, Gaussian-correlated background. We examine
free-space propagation of soft apertured realizations of the proposed beams and
show that their evolution is governed by two spatial scales: the coherence
width of the background and aperture size. A relative magnitude of these
factors determines the practical range of propagation distances over which the
novel beams can withstand diffraction. The proposed beams can find applications
to imaging and optical communications through random media.
