  We use a semi-analytic model for disk galaxies to explore the origin of the
time evolution and small scatter of the galaxy SFR sequence -- the tight
correlation between star-formation rate (SFR) and stellar mass (M_star). The
steep decline of SFR from z~2 to the present, at fixed M_star, is a consequence
of the following: First, disk galaxies are in a steady state with the SFR
following the net (i.e., inflow minus outflow) gas accretion rate. The
evolution of the SFR sequence is determined by evolution in the cosmological
specific accretion rates, \propto (1+z)^{2.25}, but is found to be independent
of feedback. Although feedback determines the outflow rates, it shifts galaxies
along the SFR sequence, leaving its zero point invariant. Second, the
conversion of accretion rate to SFR is materialized through gas density, not
gas mass. Although the model SFR is an increasing function of both gas mass
fraction and gas density, only the gas densities are predicted to evolve
significantly with redshift. Third, star formation is fueled by molecular gas.
Since the molecular gas fraction increases monotonically with increasing gas
density, the model predicts strong evolution in the molecular gas fractions,
increasing by an order of magnitude from z=0 to z~2. On the other hand, the
model predicts that the effective surface density of atomic gas is ~10 M_sun
pc^{-2}, independent of redshift, stellar mass or feedback. Our model suggests
that the scatter in the SFR sequence reflects variations in the gas accretion
history, and thus is insensitive to stellar mass, redshift or feedback. The
large scatter in halo spin contributes negligibly, because it scatters galaxies
along the SFR sequence. An observational consequence of this is that the
scatter in the SFR sequence is independent of the size (both stellar and
gaseous) of galaxy disks.
