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Denoising weak lensing mass maps with diffusion model and generative adversarial network

Shohei D. Aoyama, Ken Osato, Masato Shirasaki

TL;DR

The paper addresses the challenge of shape-noise contamination in weak-lensing mass maps by evaluating two denoising approaches: a diffusion-model (DM) and a pix2pix-based conditional GAN, using a large set of $\kappa$TNG mock WL maps. DM provides more stable training and enables multiple denoised realizations per input, yielding higher fidelity in both pixel-level reconstructions and cosmological statistics, notably recovering the angular power spectrum $C(\ell)$ up to $\ell \lesssim 6000$ and the one-point PDF more accurately than GAN. Across multiple statistics, including the bispectrum and scattering transform, DM samples show lower variance and robustness compared with GAN-derived realizations. The results imply that DM-based denoising can sharpen WL signals and support more reliable small-scale cosmological inferences from mass maps.

Abstract

The matter distribution of the Universe can be mapped through the weak gravitational lensing (WL) effect: small distortions of the shapes of distant galaxies, which reflects the inhomogeneity of the cosmic density field. The most dominant contaminant in the WL effect is the shape noise; the signal is diluted due to the finite number of source galaxies. In order to explore the full potential of WL measurements, sharpening the signal by removing the shape noise from the observational data, i.e., WL denoising, is a pressing issue. Machine learning approaches, in particular, deep generative models, have proven effective at the WL denoising task. We implement a denoising model based on the diffusion model (DM) and conduct systematic in-depth comparisons with generative adversarial networks (GANs), which have been applied in previous works for WL denoising. Utilizing the large suite of mock simulations of WL observations, we demonstrate that DM surpasses GAN in the WL denosing task in multiple aspects: (1) the training process is more stable, (2) taking the average of multiple samples from DM can robustly reproduce the true signal, and (3) DM can recover various statistics with higher accuracy.

Denoising weak lensing mass maps with diffusion model and generative adversarial network

TL;DR

The paper addresses the challenge of shape-noise contamination in weak-lensing mass maps by evaluating two denoising approaches: a diffusion-model (DM) and a pix2pix-based conditional GAN, using a large set of TNG mock WL maps. DM provides more stable training and enables multiple denoised realizations per input, yielding higher fidelity in both pixel-level reconstructions and cosmological statistics, notably recovering the angular power spectrum up to and the one-point PDF more accurately than GAN. Across multiple statistics, including the bispectrum and scattering transform, DM samples show lower variance and robustness compared with GAN-derived realizations. The results imply that DM-based denoising can sharpen WL signals and support more reliable small-scale cosmological inferences from mass maps.

Abstract

The matter distribution of the Universe can be mapped through the weak gravitational lensing (WL) effect: small distortions of the shapes of distant galaxies, which reflects the inhomogeneity of the cosmic density field. The most dominant contaminant in the WL effect is the shape noise; the signal is diluted due to the finite number of source galaxies. In order to explore the full potential of WL measurements, sharpening the signal by removing the shape noise from the observational data, i.e., WL denoising, is a pressing issue. Machine learning approaches, in particular, deep generative models, have proven effective at the WL denoising task. We implement a denoising model based on the diffusion model (DM) and conduct systematic in-depth comparisons with generative adversarial networks (GANs), which have been applied in previous works for WL denoising. Utilizing the large suite of mock simulations of WL observations, we demonstrate that DM surpasses GAN in the WL denosing task in multiple aspects: (1) the training process is more stable, (2) taking the average of multiple samples from DM can robustly reproduce the true signal, and (3) DM can recover various statistics with higher accuracy.

Paper Structure

This paper contains 4 sections, 1 equation, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Denoising mass maps with machine learning
  3. Results
  4. Conclusions

Figures (2)

  • Figure 1: Upper row: Comparison between the denoised convergence maps with GAN and DM and the ground truth map. Lower row: Zoom-in maps around the peak with the highest significance in the true noiseless map. The red squares in the maps in the upper row indicate the corresponding zoom-in regions displayed in the lower row.
  • Figure 2: Left panel: The angular power spectra of the normalised ground-truth maps (dashed line) and denoised maps (solid lines) with GAN and DM. The five blue (orange) thin lines correspond to the five networks (samples) from GAN (DM). The thick blue (orange) line shows the average power spectrum for GAN (DM). The dotted line corresponds to the noise power spectrum. The lower panel shows the fractional difference. Right panel: PDFs of the denoised maps with GAN (blue) and DM (orange). The maps are normalised so that the PDF has zero mean and unit variance.