  Traditional supervised denoisers are trained using pairs of noisy input and
clean target images. They learn to predict a central tendency of the posterior
distribution over possible clean images. When, e.g., trained with the popular
quadratic loss function, the network's output will correspond to the minimum
mean square error (MMSE) estimate. Unsupervised denoisers based on Variational
AutoEncoders (VAEs) have succeeded in achieving state-of-the-art results while
requiring only unpaired noisy data as training input. In contrast to the
traditional supervised approach, unsupervised denoisers do not directly produce
a single prediction, such as the MMSE estimate, but allow us to draw samples
from the posterior distribution of clean solutions corresponding to the noisy
input. To approximate the MMSE estimate during inference, unsupervised methods
have to create and draw a large number of samples - a computationally expensive
process - rendering the approach inapplicable in many situations. Here, we
present an alternative approach that trains a deterministic network alongside
the VAE to directly predict a central tendency. Our method achieves results
that surpass the results achieved by the unsupervised method at a fraction of
the computational cost.
