Context. Quasars at the redshift frontier ( z > 7.0) are fundamental probes of black hole growth and evolution, but are notoriously difficult to identify. At these redshifts, machine-learning-based selection methods have proven to be efficient, but require appropriate training sets to reach their full potential.

Aims. We present the variational auto-encoder QUEST, which can generate realistic quasar spectra that can be post-processed to generate synthetic photometry and impute spectra.

Methods. We started from the SDSS DR16Q catalogue, pre-processed the spectra, and vetted the sample to obtain a clean dataset. After training the model, we investigated the properties of its latent space to understand whether it has learnt the relevant physics. Furthermore, we provide a pipeline for generating photometry from the sampled spectra, which we compared with actual quasar photometry, and we show the capabilities of the model in reconstructing and extending quasar spectra.

Results. The trained network faithfully reproduces the input spectrum in terms of sample median and variance. By examining the latent space, we found correlations with continuum and bolometric luminosity, black hole mass, redshift, continuum slope, and emission line properties, among others. When we used the network to generate photometry, the results agreed very well with those from the control sample. The model provides satisfactory results in reconstructing emission lines: estimates of the black hole mass from the reconstructed spectra agree well with those from the original SDSS spectra. Furthermore, when spectra with broad absorption line features were reconstructed, the model successfully interpolated over the absorption systems. Compared with previous work, the spectra sampled from our model and the output of their results agree very well. However, QUEST does not require any ad hoc tuning and is capable of reproducing the full variety of spectra available in the training set.