Probabilistic Inference of Galaxy Parameters and Emission Lines via VAE–Normalizing Flows

The growing number of galaxies discovered in modern surveys has produced an unprecedented volume of imaging and photometric data. Extracting their physical properties typically requires spectroscopy, which is observationally expensive and computationally intensive. Building on recent advances in machine learning, we introduce a Variational Autoencoder (VAE)--Normalizing Flow framework for rapid probabilistic inference of galaxy properties and emission line fluxes at z ≲ 0.3 from SDSS gri imaging and photometry. Our model probabilistically infers stellar mass, star formation rate (SFR), redshift, gas-phase metallicity, and central black hole mass for a given galaxy. The model accuracy matches current non-spectroscopic methods for stellar mass and redshift, surpasses them for SFR and metallicity, and introduces the first probabilistic central black hole mass estimates from imaging + photometry. It also delivers probabilistic estimates of H α, H β, [N II], and [O III] emission line fluxes directly from imaging, enabling SFR, metallicity, dust, and AGN/shock diagnostics without spectroscopy. This approach opens new pathways for scalable, physics-informed inference in upcoming surveys such as Roman and Rubin LSST.