Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models

Abstract

Galaxy clusters are powerful probes of astrophysics and cosmology through gravitational lensing: the clusters' mass, dominated by 85% dark matter, distorts background light. Yet, mass reconstruction lacks the scalability and large-scale benchmarks to process the hundreds of thousands of clusters expected from forthcoming wide-field surveys. We introduce a fully automated method to reconstruct cluster surface mass density from photometry and gravitational lensing observables. Central to our approach is DarkClusters-15k, our new dataset of 15,000 simulated clusters with paired mass and photometry maps, the largest benchmark to date, spanning multiple redshifts and simulation frameworks. We train a plug-and-play diffusion prior on DarkClusters-15k that learns the statistical relationship between mass and light, and draw posterior samples constrained by weak- and strong-lensing observables; this yields principled reconstructions driven by explicit physics, alongside well-calibrated uncertainties. Our approach requires no expert tuning, runs in minutes rather than hours, achieves higher accuracy, and matches expertly-tuned reconstructions of the MACS 1206 cluster. We release our method and DarkClusters-15k to support development and benchmarking for upcoming wide-field cosmological surveys.

Figures (7)

• Figure 1: Sketch of a typical gravitational lens system. The light path of an object at angular position $\boldsymbol{\beta}$ on a source plane $S$ is deflected by $\tilde{\boldsymbol{\alpha}}$ degrees due to the presence of a galaxy cluster on the lens plane $L$, so the object appears at angular position $\boldsymbol{\theta}$ instead.
• Figure 2: Left: For the creation of our DarkClusters-15k dataset, we extract 600 simulated galaxy clusters from IllustrisTNG and SIMBA as 3D point clouds, and compute the surface mass density $\Sigma$ for $n = 25$ different line of sight $\vec{r}_i$ projections. Right: For each projection, we then independently generate measurements for strong lensing (i.e., positions of multiple images for each source) and weak lensing (i.e., shear $\boldsymbol\gamma$ at the source positions).
• Figure 3: Left: Our diffusion-based approach samples from the posterior distribution; in each row we show one representative sample of the lens convergence $\kappa$, and the posterior mean and standard deviation over 20 samples. Right: Uncertainty calibration plot, showing close correlation between our model's predicted uncertainty and the actual error.
• Figure 4: Ablation study on the different input components used by our method to estimate cluster masses. Left: Each row shows photometry $\textbf{P}_f$ for one cluster, and mass reconstructions using only one input as stated. Right: Adding strong (SL) and weak lensing (WL) information (SNR 0.01) improves the photometry (P) results. We report PSNR of each image w.r.t. the ground truth (GT).
• Figure 5: Comparison of our method with the approach by Napier et al. napier2023hubble and our UNet baseline, showing lens convergence $\kappa$ for five test samples of DarkClusters-15k at different redshifts $z_L$ and simulations. Napier et al. produce an overly smooth mass prediction, and wrongly estimates regions due to its strict 1:1 mapping of mass and photometry. Also, contrary to both the Napier et al. and our UNet baselines, our method includes gravitational lensing observables and generates samples from a posterior distribution with calibrated uncertainty estimation; we show one sample of this posterior along with the mean and std. dev. computed for 20 generated samples.