  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.
