  Solar activity is one of the main drivers of variability in our solar system
and the key source of space weather phenomena that affect Earth and near Earth
space. The extensive record of high resolution extreme ultraviolet (EUV)
observations from the Solar Dynamics Observatory (SDO) offers an unprecedented,
very large dataset of solar images. In this work, we make use of this
comprehensive dataset to investigate capabilities of current state-of-the-art
generative models to accurately capture the data distribution behind the
observed solar activity states. Starting from StyleGAN-based methods, we
uncover severe deficits of this model family in handling fine-scale details of
solar images when training on high resolution samples, contrary to training on
natural face images. When switching to the diffusion based generative model
family, we observe strong improvements of fine-scale detail generation. For the
GAN family, we are able to achieve similar improvements in fine-scale
generation when turning to ProjectedGANs, which uses multi-scale discriminators
with a pre-trained frozen feature extractor. We conduct ablation studies to
clarify mechanisms responsible for proper fine-scale handling. Using
distributed training on supercomputers, we are able to train generative models
for up to 1024x1024 resolution that produce high quality samples
indistinguishable to human experts, as suggested by the evaluation we conduct.
We make all code, models and workflows used in this study publicly available at
\url{https://github.com/SLAMPAI/generative-models-for-highres-solar-images}.
