  The study of unobscured active galactic nuclei (AGN) and quasars depends on
the reliable decomposition of the light from the AGN point source and the
extended host galaxy light. The problem is typically approached using
parametric fitting routines using separate models for the host galaxy and the
point spread function (PSF). We present a new approach using a Generative
Adversarial Network (GAN) trained on galaxy images. We test the method using
Sloan Digital Sky Survey (SDSS) r-band images with artificial AGN point sources
added which are then removed using the GAN and with parametric methods using
GALFIT. When the AGN point source PS is more than twice as bright as the host
galaxy, we find that our method, PSFGAN, can recover PS and host galaxy
magnitudes with smaller systematic error and a lower average scatter ($49\%$).
PSFGAN is more tolerant to poor knowledge of the PSF than parametric methods.
Our tests show that PSFGAN is robust against a broadening in the PSF width of
$\pm 50\%$ if it is trained on multiple PSF's. We demonstrate that while a
matched training set does improve performance, we can still subtract point
sources using a PSFGAN trained on non-astronomical images. While initial
training is computationally expensive, evaluating PSFGAN on data is more than
$40$ times faster than GALFIT fitting two components. Finally, PSFGAN it is
more robust and easy to use than parametric methods as it requires no input
parameters.
