We present coarse but robust star formation histories (SFHs) derived from spectro-photometric data of the Carnegie-Spitzer-IMACS Survey, for 22,494 galaxies at 0.3<z<0.9 with stellar masses of 10^9 Msun to 10^12 Msun. Our study moves beyond average SFHs and distribution functions of specific star formation rates (sSFRs) to individually measured SFHs for tens of thousands of galaxies. By comparing star formation rates (SFRs) with timescales of 10^10, 10^9, and 10^8 years, we find a wide diversity of SFHs: old galaxies that formed most or all of their stars early; galaxies that formed stars with declining or constant SFRs over a Hubble time, and genuinely young galaxies that formed most of their stars since z=1. This sequence is one of decreasing stellar mass, but, remarkably, each type is found over a mass range of a factor of 10. Conversely, galaxies at any given mass follow a wide range of SFHs, leading us to conclude that: (1) halo mass does not uniquely determine SFHs; (2) there is no typical evolutionary track; and (3) abundance matching has limitations as a tool for inferring physics. Our observations imply that SFHs are set at an early epoch, and that--for most galaxies--the decline and cessation of star formation occurs over a Hubble-time, without distinct quenching events. SFH diversity is inconsistent with models where galaxy mass, at any given epoch, grows simply along relations between SFR and stellar mass, but is consistent with a 2-parameter lognormal form, lending credence to this model from a new and independent perspective.
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