Strong-lensing images provide a wealth of information both about the magnified source and about the dark matter distribution in the lens. Precision analyses of these images can be used to constrain the nature of dark matter. However, this requires high-fidelity image reconstructions and careful treatment of the uncertainties of both lens mass distribution and source light, which are typically difficult to quantify. In anticipation of future high-resolution datasets, in this work we leverage a range of recent developments in machine learning to develop a new Bayesian strong-lensing image analysis pipeline. Its highlights are: (A) a fast, GPU-enabled, end-to-end differentiable strong-lensing image simulator; (B) a new, statistically principled source model based on a computationally highly efficient approximation to Gaussian processes that also takes into account pixellation; and (C) a scalable variational inference framework that enables simultaneously deriving posteriors for tens of thousands of lens and source parameters and optimising hyperparameters via stochastic gradient descent. Besides efficient and accurate parameter estimation and lens model uncertainty quantification, the main aim of the pipeline is the generation of training data for targeted simulation-based inference of dark matter substructure, which we will exploit in a companion paper.
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