  There is a remarkably tight relation between the observationally inferred
dust masses and star-formation rates (SFRs) of SDSS galaxies, Mdust $\propto$
SFR$^{1.11}$ (Da Cunha et al. 2010). Here we extend the Mdust-SFR relation to
the high end and show that it bends over at very large SFRs (i.e., dust masses
are lower than predicted for a given SFR). We identify several distinct
evolutionary processes in the diagram: (1) A star-bursting phase in which dust
builds up rapidly at early times. The maximum attainable dust mass in this
process is the cause of the bend-over of the relation. A high dust-formation
efficiency, a bottom-light initial mass function, and negligible supernova
shock dust destruction are required to produce sufficiently high dust masses.
(2) A quiescent star-forming phase in which the subsequent parallel decline in
dust mass and SFR gives rise to the Mdust-SFR relation, through astration and
dust destruction. The dust-to-gas ratio is approximately constant along the
relation. We show that the power-law slope of the Mdust-SFR relation is
inversely proportional to the global Schmidt-Kennicutt law exponent (i.e.,
$\sim 0.9$) in simple chemical evolution models. (3) A quenching phase which
causes star formation to drop while the dust mass stays roughly constant or
drops proportionally. Combined with merging, these processes, as well as the
range in total baryonic mass, give rise to a complex population of the diagram
which adds significant scatter to the original Mdust-SFR relation. (4) At very
high redshifts, a population of galaxies located significantly below the local
relation is predicted.
