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

We introduce a Variational Autoencoder (VAE)–Normalizing Flow (NF) framework for rapid probabilistic inference of galaxy properties and emission line fluxes at $z\le 0.3$ from SDSS $\mathit{\text{gri}}$ 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~$\text{textsc}ii$], and [O~$\text{textsc}iii$] 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.