  We present an efficient Bayesian method for estimating individual photometric
redshifts and galaxy properties under a pre-trained population model
(pop-cosmos) that was calibrated using purely photometric data. This model
specifies a prior distribution over 16 stellar population synthesis (SPS)
parameters using a score-based diffusion model, and includes a data model with
detailed treatment of nebular emission. We use a GPU-accelerated affine
invariant ensemble sampler to achieve fast posterior sampling under this model
for 292,300 individual galaxies in the COSMOS2020 catalog, leveraging a neural
network emulator (Speculator) to speed up the SPS calculations. We apply both
the pop-cosmos population model and a baseline prior inspired by
Prospector-$\alpha$, and compare these results to published COSMOS2020 redshift
estimates from the widely-used EAZY and LePhare codes. For the $\sim 12,000$
galaxies with spectroscopic redshifts, we find that pop-cosmos yields redshift
estimates that have minimal bias ($\sim10^{-4}$), high accuracy
($\sigma_\text{MAD}=7\times10^{-3}$), and a low outlier rate ($1.6\%$). We show
that the pop-cosmos population model generalizes well to galaxies fainter than
its $r<25$ mag training set. The sample we have analyzed is $\gtrsim3\times$
larger than has previously been possible via posterior sampling with a full SPS
model, with average throughput of 15 GPU-sec per galaxy under the pop-cosmos
prior, and 0.6 GPU-sec per galaxy under the Prospector prior. This paves the
way for principled modeling of the huge catalogs expected from upcoming Stage
IV galaxy surveys.
