Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to statistically characterize populations of point sources too dim to be individually detected. As the properties of a single dim source will be poorly constrained, instead one commonly studies the population as a whole, inferring a source-count distribution (SCD) that describes the number density of sources as a function of their brightness. Statistical and machine learning methods for recovering SCDs exist; however, they typically entirely neglect spectral information associated with the energy distribution of the flux. We present a deep learning framework able to jointly reconstruct the spectra of different emission components and the SCD of point-source populations. In a proof-of-concept example, we show that our method accurately extracts even complex-shaped spectra and SCDs from simulated maps.

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.