Very-Long Baseline Interferometry Imaging with Closure Invariants using Conditional Image Diffusion

Image reconstruction in very-long baseline interferometry operates under severely sparse aperture coverage with calibration challenges from both the participating instruments and propagation medium, which introduce the risk of biases and artefacts. Interferometric closure invariants offers calibration-independent information on the true source morphology, but the inverse transformation from closure invariants to the source intensity distribution is an ill-posed problem. In this work, we present a generative deep learning approach to tackle the inverse problem of directly reconstructing images from their observed closure invariants. Trained in a supervised manner with simple shapes and the CIFAR-10 dataset, the resulting trained model achieves reduced chi-square data adherence scores of $\chi^2_{\rm CI} \lesssim 1$ and maximum normalised cross-correlation image fidelity scores of $\rho_{\rm NX} > 0.9$ on tests of both trained and untrained morphologies, where $\rho_{\rm NX}=1$ denotes a perfect reconstruction. We also adapt our model for the Next Generation Event Horizon Telescope total intensity analysis challenge. Our results on quantitative metrics are competitive to other state-of-the-art image reconstruction algorithms. As an algorithm that does not require finely hand-tuned hyperparameters, this method offers a relatively simple and reproducible calibration-independent imaging solution for very-long baseline interferometry, which ultimately enhances the reliability of sparse VLBI imaging results.