Denoising weak lensing mass maps with the diffusion model: Systematic comparison with the generative adversarial network

Abstract Weak gravitational lensing (WL) is a unique and powerful probe into the large-scale structures of the Universe. Removing the shape noise from the observed WL field, i.e., denoising, enhances the potential of WL by accessing information at small scales where the shape noise dominates without denoising. We utilise two machine learning (ML) models for denoising: the generative adversarial network (GAN) and the diffusion model (DM). We evaluate the performance of denoising with GAN and DM utilising a large suite of mock WL observations, which serve as the training and test data sets. We apply denoising to 1000 noisy mass maps with GAN and DM models trained using 39000 mock observations. Both models can reproduce the true convergence map fairly well on large scales. Then, we measure cosmological statistics: power spectrum, bispectrum, one-point probability distribution function, peak and minima counts, and scattering transform coefficients. We find that DM outperforms GAN in almost all considered statistics and recovers the correct statistics down to small scales. For example, the angular power spectrum can be recovered with DM up to multipoles $\ell \lesssim 6000$ while the noise power spectrum dominates from $\ell \simeq 2000$. We also conduct stress tests on the trained model; denoising the maps with different characteristics, e.g., different source redshifts, from the training data. The performance degrades at small scales, but the statistics can still be recovered at large scales. Though the training of DM is more computationally demanding compared with GAN, there are several advantages: numerically stable training, higher performance in the reconstruction of cosmological statistics, and sampling multiple realisations once the model is trained. It has been known that DM can generate higher-quality images in real-world problems than GAN; the superiority has been confirmed as well in the WL denoising problem.