Generative Diffusion Priors for 3D Mapping of the Dark Universe

2026-05-30

AI Summary

This work addresses the highly ill-posed inverse problem of reconstructing the three-dimensional dark matter distribution from weak gravitational lensing observations, which is fundamentally limited by single-line-of-sight measurements, shape noise, and photometric redshift uncertainties. The authors propose a Bayesian posterior sampling framework based on diffusion models, integrating a differentiable physical forward model with a data-driven, three-dimensional generative prior. This prior is trained on the high-fidelity Conicus3D dataset derived from cosmological simulations and effectively captures the non-Gaussian, filamentary structure of the cosmic web. Experiments on simulated data mimicking modern weak lensing surveys demonstrate that the method substantially outperforms existing two- and three-dimensional reconstruction techniques, yielding posterior samples whose statistical properties closely match those of the ground-truth simulations and exhibiting robustness to shifts in cosmological parameters.

Abstract

Reconstructing the three-dimensional distribution of dark matter from weak-lensing observations is a central but highly ill-posed inverse problem in cosmology. Unlike standard 3D reconstruction with multiple viewpoints, we observe the universe from a single line of sight, through noisy shape distortions of galaxies with uncertain distances, so meaningful recovery of the 3D matter field requires strong prior assumptions. Existing methods either produce point estimates with handcrafted priors or use neural ensembles for approximate Bayesian uncertainty, and struggle to capture the non-Gaussian, filamentary structure of the cosmic web. With the advent of new high-resolution cosmological simulations, we now have an alternative source of prior knowledge that captures the nonlinear statistics of structure formation with far greater fidelity than analytic prescriptions. We leverage these simulations to build a new dataset $\texttt{Conicus3D}$, which enables us to learn a data-driven diffusion-model prior capturing the full 3D distribution of dark matter structure across cosmic time. Building on recent plug-and-play approaches, we modify a diffusion-based posterior sampling scheme to the 3D weak-lensing setting, combining the learned prior with a differentiable physical forward model. On realistic simulations targeting a modern weak lensing survey, our approach yields substantially improved 2D and 3D reconstruction accuracy over baseline methods. Moreover, it produces posterior samples whose statistics closely track the underlying simulations, while remaining robust to moderate shifts in cosmology.

Problem

• 3D dark matter mapping
• weak gravitational lensing
• inverse problem
• cosmic web
• non-Gaussian structure

Innovation

• generative diffusion prior
• 3D weak-lensing reconstruction
• data-driven cosmological prior
• posterior sampling
• Conicus3D dataset