On the Posterior Gap in Plug & Play Diffusion Methods for Sparse-View Computed Tomography

Recent advances in conditional diffusion models have demonstrated impressive performance on inverse problems such as Sparse-View Computed Tomography (SVCT), typically evaluated using estimation error metrics like PSNR or SSIM. However, in ultra-sparse regimes, where the number of projections is extremely limited, the sinogram is weakly informative resulting in high variability in posterior samples. This is especially true in applications involving dynamic phenomena, such as imaging the exhaust gas from a nozzle, where only a handful of projections can be captured simultaneously. In this context, evaluation based solely on estimation error (e.g. PSNR/SSIM) is no longer adequate. To address this limitation and complement the PSNR/SSIM evaluation, we propose to evaluate the Posterior Gap (PG), which measures the discrepancy between the true posterior distribution and the approximation induced by a given generative model. We introduce a practical framework for PG estimation using only prior samples, the observation model, and posterior samples. We consider three state-of-theart Plug & Play diffusion models DPS,$\prod$G, and FPS. Since DPS includes a sensitive hyperparameter, we present a simple calibration strategy to reduce the PG. Our study benchmarks DPS,$\prod$G and FPS across three SVCT datasets. Results show that when carefully calibrated, DPS outperforms FPS and$\prod$G. By complementing traditional metrics, our evaluation protocol offers a more comprehensive understanding of reconstruction performance, particularly in severely ill-posed regimes such as dynamic gas imaging with six or fewer projections.