  Image denoising and artefact removal are complex inverse problems admitting
many potential solutions. Variational Autoencoders (VAEs) can be used to learn
a whole distribution of sensible solutions, from which one can sample
efficiently. However, such a generative approach to image restoration is only
studied in the context of pixel-wise noise removal (e.g. Poisson or Gaussian
noise). While important, a plethora of application domains suffer from imaging
artefacts (structured noises) that alter groups of pixels in correlated ways.
In this work we show, for the first time, that generative diversity denoising
(GDD) approaches can learn to remove structured noises without supervision. To
this end, we investigate two existing GDD architectures, introduce a new one
based on hierarchical VAEs, and compare their performances against a total of
seven state-of-the-art baseline methods on five sources of structured noise
(including tomography reconstruction artefacts and microscopy artefacts). We
find that GDD methods outperform all unsupervised baselines and in many cases
not lagging far behind supervised results (in some occasions even superseding
them). In addition to structured noise removal, we also show that our new GDD
method produces new state-of-the-art (SOTA) results on seven out of eight
benchmark datasets for pixel-noise removal. Finally, we offer insights into the
daunting question of how GDD methods distinguish structured noise, which we
like to see removed, from image signals, which we want to see retained.
