# Probabilistic Mass Mapping with Neural Score Estimation

arXiv: https://arxiv.org/abs/2201.05561 · HTML: https://mlsanity.com/paper/2201.05561/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 23 references that are in the map.
- First posted on arXiv 14 Jan 2022.

## Builds on (most cited first, 2 of 2)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)

## Built on by (most cited first, 17 of 17)

- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Posterior samples of source galaxies in strong gravitational lenses with score-based priors](https://mlsanity.com/paper/2211.03812/) (2022)
- [Astronomia ex machina: a history, primer, and outlook on neural networks in astronomy](https://mlsanity.com/paper/2211.03796/) (2022)
- [Can denoising diffusion probabilistic models generate realistic astrophysical fields?](https://mlsanity.com/paper/2211.12444/) (2022)
- [PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation](https://mlsanity.com/paper/2402.04355/) (2024)
- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
- [Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems](https://mlsanity.com/paper/2407.17667/) (2024)
- [Diffusion Models for Probabilistic Deconvolution of Galaxy Images](https://mlsanity.com/paper/2307.11122/) (2023)
- [Bayesian Imaging for Radio Interferometry with Score-Based Priors](https://mlsanity.com/paper/2311.18012/) (2023)
- [Diffusion-HMC: Parameter Inference with Diffusion-model-driven Hamiltonian Monte Carlo](https://mlsanity.com/paper/2405.05255/) (2024)
- [Echoes in the Noise: Posterior Samples of Faint Galaxy Surface Brightness Profiles with Score-Based Likelihoods and Priors](https://mlsanity.com/paper/2311.18002/) (2023)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models](https://mlsanity.com/paper/2603.14503/) (2026)
- [MIRA: A Score for Conditional Distribution Accuracy and Model Comparison](https://mlsanity.com/paper/2605.02014/) (2026)
- [Uncertainty-Aware Blob Detection with an Application to Integrated-Light Stellar Population Recoveries](https://mlsanity.com/paper/2208.05881/) (2022)
- [Generative Diffusion Priors for 3D Mapping of the Dark Universe](https://mlsanity.com/paper/2606.00803/) (2026)
- [Graph Residual Conjugate Diffusion: SNR-Equalized Heat Flow for Graph Signals](https://mlsanity.com/paper/2609.39658/) (2026)

## Abstract (arXiv)

Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging ill-posed inverse problem. We introduce a novel methodology allowing for efficient sampling of the high-dimensional Bayesian posterior of the weak lensing mass-mapping problem, and relying on simulations for defining a fully non-Gaussian prior. We aim to demonstrate the accuracy of the method on simulations, and then proceed to applying it to the mass reconstruction of the HST/ACS COSMOS field. The proposed methodology combines elements of Bayesian statistics, analytic theory, and a recent class of Deep Generative Models based on Neural Score Matching. This approach allows us to do the following: 1) Make full use of analytic cosmological theory to constrain the 2pt statistics of the solution. 2) Learn from cosmological simulations any differences between this analytic prior and full simulations. 3) Obtain samples from the full Bayesian posterior of the problem for robust Uncertainty Quantification. We demonstrate the method on the kappaTNG simulations and find that the posterior mean significantly outperfoms previous methods (Kaiser-Squires, Wiener filter, Sparsity priors) both on root-mean-square error and in terms of the Pearson correlation. We further illustrate the interpretability of the recovered posterior by establishing a close correlation between posterior convergence values and SNR of clusters artificially introduced into a field. Finally, we apply the method to the reconstruction of the HST/ACS COSMOS field and yield the highest quality convergence map of this field to date.