In recent years, deep learning models have been successfully employed for
augmenting low-resolution cosmological simulations with small-scale
information, a task known as "super-resolution". So far, these cosmological
super-resolution models have relied on generative adversarial networks (GANs),
which can achieve highly realistic results, but suffer from various
shortcomings (e.g. low sample diversity). We introduce denoising diffusion
models as a powerful generative model for super-resolving cosmic large-scale
structure predictions (as a first proof-of-concept in two dimensions). To
obtain accurate results down to small scales, we develop a new "filter-boosted"
training approach that redistributes the importance of different scales in the
pixel-wise training objective. We demonstrate that our model not only produces
convincing super-resolution images and power spectra consistent at the percent
level, but is also able to reproduce the diversity of small-scale features
consistent with a given low-resolution simulation. This enables uncertainty
quantification for the generated small-scale features, which is critical for
the usefulness of such super-resolution models as a viable surrogate model for
cosmic structure formation.

近年来，深度学习模型成功应用于增强低分辨率宇宙学模拟的小尺度信息，称为 “超分辨”。我们引入去噪扩散模型作为一种强大的生成模型，用于超分辨宇宙大尺度结构预测（首次在二维中作为概念验证）。通过开发一种新的 “滤波增强” 训练方法，重分配了像素级训练目标中不同尺度的重要性，以获得准确的小尺度结果。我们证明了我们的模型不仅能够产生令人信服的超分辨图像和功率谱，保持百分位水平的一致性，还能够重现与给定低分辨率模拟一致的小尺度特征的多样性，这对于这种超分辨模型作为宇宙结构形成的替代模型的有效性来说至关重要。