Abstract: State-of-the-art spectral energy distribution (SED) analyses use Bayesian inference to derive physical properties of galaxies from observed photometry or spectra. They require sampling from a high-dimensional space of model parameters and take $>10-100$ CPU hours per galaxy. This renders them practically infeasible for analyzing the {\em 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 approach using Amortized Neural Posterior Estimation (ANPE). ANPE is a likelihood-free inference method that employs neural networks to estimate the posterior over the full range of observations. Once trained, it requires no additional model evaluations to estimate the posterior. We present SEDflow, an ANPE method to produce posteriors of the recent Hahn et al. (2022) SED model from optical photometry and spectra. SEDflow 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.