Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models

TL;DR

This work tackles blind strong-lensing inversion by jointly inferring a background source and a parametric lens mass using score-based priors. It develops a continuous-time GibbsDDRM-inspired sampler that alternates updates to the source via a likelihood-score method (either $\Pi$GDM or CLA) and updates lens parameters via gradient-based methods, guided by a VE diffusion model. The study validates the approach on simulated data, showing residuals that match the noise distribution and marginal lens posteriors that are unbiased with respect to true parameters, demonstrating robust handling of nonlinearities and degeneracies. This framework enables fully Bayesian joint inference for upcoming large-scale lens surveys (LSST, Euclid), facilitating rigorous cosmological and astrophysical analyses from lensing data.

Abstract

Score-based models can serve as expressive, data-driven priors for scientific inverse problems. In strong gravitational lensing, they enable posterior inference of a background galaxy from its distorted, multiply-imaged observation. Previous work, however, assumes that the lens mass distribution (and thus the forward operator) is known. We relax this assumption by jointly inferring the source and a parametric lens-mass profile, using a sampler based on GibbsDDRM but operating in continuous time. The resulting reconstructions yield residuals consistent with the observational noise, and the marginal posteriors of the lens parameters recover true values without systematic bias. To our knowledge, this is the first successful demonstration of joint source-and-lens inference with a score-based prior.

Figures (9)

• Figure 1: Simulated strong-lensing system analyzed with our joint sampler. Top-right panel: the observed image $\mathbf{y}$, the true source $\mathbf{x}^{\star}$, and three joint-posterior draws $(\mathbf{x}_i,\boldsymbol{\ell}_i)$. For each draw we show the reconstructed image $A_{\boldsymbol{\ell}_i}\mathbf{x}_i$ and the corresponding residual $(\mathbf{y}-A_{\boldsymbol{\ell}_i}\mathbf{x}_i)/\sigma_{\boldsymbol{\eta}}$, demonstrating noise-level consistency. Bottom-left panel: marginal lens posterior $p(\boldsymbol{\ell}\mid\mathbf{y})$ obtained from $406$ joint samples, each augmented with $500$ conditional lens draws as described in \ref{['app:marginal_posterior']}.
• Figure 2: Marginal lens posterior $p(\boldsymbol{\ell}\mid\mathbf{y})$ (black contours and histograms) compared with six conditional posteriors $p(\boldsymbol{\ell}\mid\mathbf{y},\mathbf{x})$ (colored curves), where each $\mathbf{x}$ is drawn from the joint sampler. Only the parameters $\theta_{\mathrm{E}}$ and $\tau$ are shown for clarity.
• Figure 3: Source-only inference variables with CLA at $t=0.5$.
• Figure 4: Source-only inference variables with $\Pi$GDM at $t=0.5$.
• Figure 5: Evolution of the Tweedie posterior mean $\hat{\mathbf{x}}_{t}$ during $\Pi$GDM source-only inference.