Can Diffusion Model Conditionally Generate Astrophysical Images?

Generative adversarial networks (GANs) are frequently utilized in astronomy to construct an emulator of numerical simulations. Nevertheless, training GANs can prove to be a precarious task, as they are prone to instability and often lead to mode collapse problems. Conversely, the diffusion model also has the ability to generate high-quality data without adversarial training. It has shown superiority over GANs with regard to several natural image datasets. In this study, we undertake a quantitative comparison between the denoising diffusion probabilistic model (DDPM) and StyleGAN2 (one of the most robust types of GANs) via a set of robust summary statistics from scattering transform. In particular, we utilize both models to generate the images of 21 cm brightness temperature mapping, as a case study, conditionally based on astrophysical parameters that govern the process of cosmic reionization. Using our new Fr\'echet Scattering Distance (FSD) as the evaluation metric to quantitatively compare the sample distribution between generative models and simulations, we demonstrate that DDPM outperforms StyleGAN2 on varied sizes of training sets. Through Fisher forecasts, we demonstrate that on our datasets, StyleGAN2 exhibits mode collapses in varied ways, while DDPM yields a more robust generation. We also explore the role of classifier-free guidance in DDPM and show the preference for a non-zero guidance scale only when the training data is limited. Our findings indicate that the diffusion model presents a promising alternative to GANs in the generation of accurate images. These images can subsequently provide reliable parameter constraints, particularly in the realm of astrophysics.