All-sky searches for continuous gravitational waves are generally model dependent and computationally costly to run. By contrast, SOAP is a model-agnostic search that rapidly returns candidate signal tracks in the time-frequency plane. In this work we extend the SOAP search to return broad Bayesian posteriors on the astrophysical parameters of a specific signal model. These constraints drastically reduce the volume of parameter space that any follow-up search needs to explore, so increasing the speed at which candidates can be identified and confirmed. Our method uses a machine learning technique, specifically a conditional variational auto-encoder, and delivers a rapid estimation of the posterior distribution of the four Doppler parameters of a continuous wave signal. It does so without requiring a clear definition of a likelihood function, or being shown any true Bayesian posteriors in training. We demonstrate how the Doppler parameter space volume can be reduced by a factor of
for signals of SNR 100.