A New Census of the 0.2< z <3.0 Universe, Part II: The Star-Forming
  Sequence
  We use the panchromatic SED-fitting code Prospector to measure the galaxy
logM$^*$-logSFR relationship (the `star-forming sequence') across $0.2 < z <
3.0$ using the COSMOS-2015 and 3D-HST UV-IR photometric catalogs. We
demonstrate that the chosen method of identifying star-forming galaxies
introduces a systematic uncertainty in the inferred normalization and width of
the star-forming sequence, peaking for massive galaxies at $\sim 0.5$ dex and
$\sim0.2$ dex respectively. To avoid this systematic, we instead parameterize
the density of the full galaxy population in the logM$^*$-logSFR-redshift plane
using a flexible neural network known as a normalizing flow. The resulting
star-forming sequence has a low-mass slope near unity and a much flatter slope
at higher masses, with a normalization $0.2-0.5$ dex lower than typical
inferences in the literature. We show this difference is due to the
sophistication of the Prospector stellar populations modeling: the
nonparametric star formation histories naturally produce higher masses while
the combination of individualized metallicity, dust, and star formation history
constraints produce lower star formation rates than typical UV+IR formulae. We
introduce a simple formalism to understand the difference between SFRs inferred
from spectral energy distribution fitting and standard template-based
approaches such as UV+IR SFRs. Finally, we demonstrate the inferred
star-forming sequence is consistent with predictions from theoretical models of
galaxy formation, resolving a long-standing $\sim0.2-0.5$ dex offset with
observations at $0.5<z<3$. The fully trained normalizing flow including a
nonparametric description of $\rho(\log{\rm M}^*,\log{\rm SFR},z)$ is made
available online to facilitate straightforward comparisons with future work.
