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

Adiba Amira Siddiqa, Sayed Shafaat Mahmud, Rafael Martinez-Galarza

TL;DR

The paper addresses the challenge of inferring galaxy physical properties and emission-line fluxes from imaging data, offering calibrated probabilistic posteriors rather than point estimates. It introduces a VAE–NF framework where a VAE encodes images into latent features that are fed into two conditional normalizing flows to jointly infer core properties (Mstar, SFR, z, MBH, metallicity) and emission-line fluxes, using a training dataset of SDSS galaxies with z ≤ 0.3. The approach yields strong accuracy (e.g., Mstar, z, metallicity, and Balmer lines) and provides first probabilistic MBH mass estimates from imaging, while delivering 100× faster inference than traditional SED fitting. This scalable, physics-informed pipeline enables spectroscopy-free diagnostics for upcoming surveys such as Roman Space Telescope and Rubin LSST, with calibrated posteriors and preserved parameter correlations.

Abstract

We introduce a Variational Autoencoder (VAE)--Normalizing Flow (NF) 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$α$, H$β$, [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.

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

TL;DR

The paper addresses the challenge of inferring galaxy physical properties and emission-line fluxes from imaging data, offering calibrated probabilistic posteriors rather than point estimates. It introduces a VAE–NF framework where a VAE encodes images into latent features that are fed into two conditional normalizing flows to jointly infer core properties (Mstar, SFR, z, MBH, metallicity) and emission-line fluxes, using a training dataset of SDSS galaxies with z ≤ 0.3. The approach yields strong accuracy (e.g., Mstar, z, metallicity, and Balmer lines) and provides first probabilistic MBH mass estimates from imaging, while delivering 100× faster inference than traditional SED fitting. This scalable, physics-informed pipeline enables spectroscopy-free diagnostics for upcoming surveys such as Roman Space Telescope and Rubin LSST, with calibrated posteriors and preserved parameter correlations.

Abstract

We introduce a Variational Autoencoder (VAE)--Normalizing Flow (NF) framework for rapid probabilistic inference of galaxy properties and emission line fluxes at 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, H, [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.

Paper Structure

This paper contains 9 sections, 1 equation, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data Selection and Preprocessing
  4. Variational Autoencoder Architecture
  5. Two-Stage Conditional Normalizing Flow Framework
  6. Results
  7. Conclusion and Future Work
  8. Acknowledgements
  9. Posterior Distribution Example

Figures (5)

  • Figure 1: VAE–NF hybrid architecture
  • Figure 2: Predicted versus true values for galaxy properties and emission-line fluxes. Each panel compares model predictions against ground truth, with the dashed red line indicating the one-to-one relation.
  • Figure 3: Perturbational decoding of redshift and SFR of a representative galaxy. As we increase redshift, we see the galaxy getting smaller and farther away. As we decrease SFR, we see the galaxy obtaining a yellower bulge which is a common characteristic of galaxies with lower SFR.
  • Figure 4: UMAP embeddings of galaxies when only images are used (a, c) and when images are combined with photometric information (b,d) for stellar mass and mass of central Black hole. For both cases, photometry significantly helps distinguish high mass and low mass cases in UMAP embeddings highlighting photometry's role in parameter inference.
  • Figure 5: Posterior distributions for a representative galaxy. Diagonal panels show marginalized 1D posteriors; off-diagonals show 2D contours. (a) Correlations between stellar mass, SFR, and redshift. (b) Joint posterior over emission-line fluxes (log$(1+\mathrm{flux})$ units).