2026ApJ...997..225M

Dust-continuum observations of many protoplanetary disks (PPDs) reveal rings and gaps that are widely interpreted as evidence of ongoing planet formation. Here we present the first framework for inferring planet and disk parameters from such images using variational autoencoder (VAE)-based generative machine learning. The new framework is called Variational Autoencoder for Disks with Embedded Rings (VADER). We train VADER on synthetic images of dust-continuum emission, generated from FARGO3D hydrodynamic simulations postprocessed with Monte Carlo radiative-transfer calculations. VADER infers the masses of up to three embedded planets as well as the disk parameters α-viscosity, dust-to-gas ratio, Stokes number, and flaring index. VADER returns a full posterior distribution for each of these quantities. We demonstrate that VADER reconstructs disk morphologies with high structural similarity (index > 0.99), accurately recovers planet parameters with R² > 0.9 across planet masses, and reliably predicts disk parameters. Applied to Atacama Large Millimeter/submillimeter Array (ALMA) dust-continuum images of 23 PPDs, our model returns mass estimates for embedded planets of 0.3-2 M_Jup that agree to within 1σ of published values in most cases, and infers disk parameters consistent with current literature. Once trained, the VAE performs full posterior parameter inference in a matter of minutes, offering statistical rigor with enough computational speed for application to large-scale ALMA surveys. These results establish VAE-based models as powerful tools for inferring from disk structure the masses of embedded planets and the global disk parameters, with their associated uncertainties.