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.
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