Galaxy imaging with generative models: insights from a two-models framework

ABSTRACT Generative models have recently revolutionized image generation tasks across diverse domains, including galaxy image synthesis. This study investigates the statistical learning and consistency of three generative models: light-weight-gan (a generative adversarial network (GAN)-based model), Glow (a normalizing flow-based model), and a diffusion model based on a U-Net denoiser, all trained on non-overlapping subsets of the Sloan Digital Sky Survey data set of $64 \times 64$ greyscale images. While all models produce visually realistic images with well-preserved morphological variable distributions, we focus on their ability to learn and generalize the underlying data distribution. The diffusion model shows a transition from memorization to generalization as the data set size increases, confirming previous findings. Smaller data sets lead to overfitting, while larger data sets enable novel sample generation, supported by the denoizing process’s theoretical basis. For the flow-based model, we propose an ‘inversion test’ leveraging its bijective nature. Similarly, the GAN-based model achieves comparable morphological consistency but lacks bijectivity. We then introduce a ‘discriminator test,’ which shows successful learning for larger data sets but poorer confidence with smaller ones. Across all models, data set sizes below $O(10^5)$ pose challenges to learning. Along our experiments, the ‘two-models’ framework enables robust evaluations, highlighting both the potential and limitations of these models. These findings provide valuable insights into statistical learning in generative modelling, with applications certainly extending beyond galaxy image generation.