  State-of-the-art spectral energy distribution (SED) analyses use a Bayesian
framework to infer the physical properties of galaxies from observed photometry
or spectra. They require sampling from a high-dimensional space of SED model
parameters and take $>10-100$ CPU hours per galaxy, which renders them
practically infeasible for analyzing the $billions$ of galaxies that will be
observed by upcoming galaxy surveys ($e.g.$ DESI, PFS, Rubin, Webb, and Roman).
In this work, we present an alternative scalable approach to rigorous Bayesian
inference using Amortized Neural Posterior Estimation (ANPE). ANPE is a
simulation-based inference method that employs neural networks to estimate the
posterior probability distribution over the full range of observations. Once
trained, it requires no additional model evaluations to estimate the posterior.
We present, and publicly release, ${\rm SED}{flow}$, an ANPE method to produce
posteriors of the recent Hahn et al. (2022) SED model from optical photometry.
${\rm SED}{flow}$ takes ${\sim}1$ $second~per~galaxy$ to obtain the posterior
distributions of 12 model parameters, all of which are in excellent agreement
with traditional Markov Chain Monte Carlo sampling results. We also apply ${\rm
SED}{flow}$ to 33,884 galaxies in the NASA-Sloan Atlas and publicly release
their posteriors: see https://changhoonhahn.github.io/SEDflow.
