  We present a forward modeling framework for estimating galaxy redshift
distributions from photometric surveys. Our forward model is composed of: a
detailed population model describing the intrinsic distribution of physical
characteristics of galaxies, encoding galaxy evolution physics; a stellar
population synthesis model connecting the physical properties of galaxies to
their photometry; a data-model characterizing the observation and calibration
processes for a given survey; and, explicit treatment of selection cuts, both
into the main analysis sample and subsequent sorting into tomographic redshift
bins. This approach has the appeal that it does not rely on spectroscopic
calibration data, provides explicit control over modeling assumptions, and
builds a direct bridge between photo-$z$ inference and galaxy evolution
physics. In addition to redshift distributions, forward modeling provides a
framework for drawing robust inferences about the statistical properties of the
galaxy population more generally. We demonstrate the utility of forward
modeling by estimating the redshift distributions for the Galaxy And Mass
Assembly (GAMA) and Vimos VLT Deep (VVDS) surveys, validating against their
spectroscopic redshifts. Our baseline model is able to predict tomographic
redshift distributions for GAMA and VVDS with a bias of $\Delta z \lesssim
0.003$ and $\Delta z \simeq 0.01$ on the mean redshift respectively --
comfortably accurate enough for Stage III cosmological surveys -- without any
hyper-parameter tuning (i.e., prior to doing any fitting to those data). We
anticipate that with additional hyper-parameter fitting and modeling
improvements, forward modeling can provide a path to accurate redshift
distribution inference for Stage IV surveys.
