From Images to Physics: Probabilistic Inference of Galaxy Parameters and Emission Lines via VAE–Normalizing Flows

We introduce a Variational Autoencoder (VAE)--Normalizing Flow framework for rapid probabilistic inference of galaxy properties and emission line fluxes at $z \leq 0.3$ from SDSS \textit{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 accruacy 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$\alpha$, H$\beta$, [N~\textsc{ii}], and [O~\textsc{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.