  The measurement of the structure of stellar populations in the Milky Way disk
places fundamental constraints on models of galaxy formation and evolution.
Previously, the disk's structure has been studied in terms of populations
defined geometrically and/or chemically, but a decomposition based on stellar
ages provides a more direct connection to the history of the disk, and stronger
constraint on theory. Here, we use positions, abundances and ages for 31,244
red giant branch stars from the SDSS-APOGEE survey, spanning $3 <
R_{\mathrm{gc}} < 15$ kpc, to dissect the disk into mono-age and mono-[Fe/H]
populations at low and high [$\alpha$/Fe]. For each population, with $\Delta
\mathrm{age} < 2$ Gyr and $\Delta \mathrm{[Fe/H]} < 0.1$ dex, we measure the
structure and surface-mass density contribution. We find that low [$\alpha$/Fe]
mono-age populations are fit well by a broken exponential, which increases to a
peak radius and decreases thereafter. We show that this profile becomes broader
with age, interpreted here as a new signal of disk heating and radial
migration. High [$\alpha$/Fe] populations are well fit as single exponentials
within the radial range considered, with an average scale length of $1.9\pm
0.1$ kpc. We find that the relative contribution of high to low [$\alpha$/Fe]
populations at $R_0$ is $f_\Sigma = 18\% \pm 5\%$; high [$\alpha$/Fe]
contributes most of the mass at old ages, and low [$\alpha$/Fe] at young ages.
The low and high [$\alpha$/Fe] populations overlap in age at intermediate
[Fe/H], although both contribute mass at $R_{0}$ across the full range of
[Fe/H]. The mass weighted scale height $h_Z$ distribution is a smoothly
declining exponential function. High [$\alpha$/Fe] populations are thicker than
low [$\alpha$/Fe], and the average $h_Z$ increases steadily with age, between
200 and 600 pc.
