Title: Employing Generative Diffusion Priors to Map the Dark Universe in Three Dimensions

Reconstructing the three-dimensional arrangement of dark matter using weak-lensing data represents a pivotal yet severely ill-posed inverse challenge within the field of cosmology. Because astronomers view the cosmos from a single line of sight—relying on noisy shape distortions of galaxies with ambiguous distances—successful recovery of the 3D matter field depends heavily on robust prior assumptions. This differs significantly from conventional 3D reconstruction tasks that utilize multiple viewpoints.

Current methodologies generally fall into two categories: they either generate point estimates based on manually designed priors or employ neural ensembles to estimate Bayesian uncertainty approximately. Both approaches face difficulties in accurately depicting the non-Gaussian, filamentary architecture of the cosmic web. However, the emergence of high-resolution cosmological simulations offers a novel source of prior knowledge. These simulations capture the nonlinear statistics of structure formation with significantly higher fidelity than traditional analytic prescriptions.

Capitalizing on these simulations, we have developed a new dataset named $\texttt{Conicus3D}$. This resource allows us to train a data-driven diffusion-model prior that encapsulates the complete 3D distribution of dark matter structures throughout cosmic history. By adapting recent plug-and-play techniques, we have tailored a diffusion-based posterior sampling framework specifically for the 3D weak-lensing context. This method integrates our learned prior with a differentiable physical forward model.

Tests on realistic simulations designed for a contemporary weak-lensing survey demonstrate that our approach achieves markedly better reconstruction accuracy in both two and three dimensions compared to baseline methods. Furthermore, the posterior samples generated by our model exhibit statistics that closely align with those of the underlying simulations and maintain robustness against moderate variations in cosmological parameters.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC