  In the majority of GAN architectures, the latent space is defined as a set of
vectors of given dimensionality. Such representations are not easily
interpretable and do not capture spatial information of image content directly.
In this work, we define a family of spatial latent spaces for StyleGAN2,
capable of capturing more details and representing images that are
out-of-sample in terms of the number and arrangement of object parts, such as
an image of multiple faces or a face with more than two eyes. We propose a
method for encoding images into our spaces, together with an attribute model
capable of performing attribute editing in these spaces. We show that our
spaces are effective for image manipulation and encode semantic information
well. Our approach can be used on pre-trained generator models, and attribute
edition can be done using pre-generated direction vectors making the barrier to
entry for experimentation and use extremely low. We propose a regularization
method for optimizing latent representations, which equalizes distributions of
parts of latent spaces, making representations much closer to generated ones.
We use it for encoding images into spatial spaces to obtain significant
improvement in quality while keeping semantics and ability to use our attribute
model for edition purposes. In total, using our methods gives encoding quality
boost even as high as 30% in terms of LPIPS score comparing to standard
methods, while keeping semantics. Additionally, we propose a StyleGAN2 training
procedure on our spatial latent spaces, together with a custom spatial latent
representation distribution to make spatially closer elements in the
representation more dependent on each other than farther elements. Such
approach improves the FID score by 29% on SpaceNet, and is able to generate
consistent images of arbitrary sizes on spatially homogeneous datasets, like
satellite imagery.
