Feed-Forward Hierarchical Gaussian Diffusion for Extreme CT Reconstruction

Reconstructing three-dimensional computed tomography (CT) from severely constrained projections is highly ill-posed. Sparse angular sampling, restricted angular coverage, and low photon counts can occur individually or jointly, obscuring global anatomy and local tissue detail. Many learned CT reconstruction methods are tailored to a single dominant degradation. Existing diffusion and Gaussian approaches commonly recover global structure and local detail within a shared representation. We propose HiGDiff, a feed-forward hierarchical Gaussian diffusion framework that decomposes reconstruction both spatially and from structure to detail. Physics-conditioned anatomical anchors and a foreground capacity field allocate learnable Gaussian primitives to informative regions. A structure diffusion stage first recovers global attenuation geometry, and its learned representation conditions a detail diffusion stage for residual boundaries and tissue transitions. The resulting Gaussian banks are rendered as attenuation fields and further refined by a gradient-isolated residual module. Experiments on three distinct CT benchmark datasets demonstrate state-of-the-art reconstruction performance across isolated, paired, and joint degradation settings, including improvements of 5.81 dB in macro-average peak signal-to-noise ratio (PSNR) and 0.113 in structural similarity index measure (SSIM) on the Low Dose CT Image and Projection Data (LDCT-PD) collection. Code and experimental configurations are openly available at https://github.com/Bean-Young/HiGDiff.