X-ray imaging is indispensable in medical diagnostics, yet its use is tightly regu-ectilated due to radiation exposure.

Solving inverse problems--recovering signals from incomplete or noisy measurements--is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System-embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Widely adopted evaluation metrics for sparse-view CT reconstruction, such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio, prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, small organs, intestines, and vessels. Building on these metrics, we introduce CARE, a Completeness-Aware Reconstruction Enhancement framework that incorporates structural penalties during training to encourage anatomical preservation of significant structures. CARE is model-agnostic and can be seamlessly integrated into analytical, implicit, and generative methods.

Figure 1: Training the proposed Patch Diffusion Inverse Solver (PaDIS) method. Different sized patches are used in each training iteration.

Deep learning has brought significant advancements to X-ray Computed Tomography (CT) reconstruction, offering solutions to challenges arising from modern imaging technologies. These developments benefit from methods that combine classical reconstruction techniques with data-driven approaches. Differentiable operators play a key role in this integration by enabling end-to-end optimization and the incorporation of physical modeling within neural networks. In this work, we present an updated version of PYRO-NN, a Python-based library for differentiable CT reconstruction. The updated framework extends compatibility to PyTorch and introduces native CUDA kernel support for efficient projection and back-projection operations across parallel, fan, and cone-beam geometries. Additionally, it includes tools for simulating imaging artifacts, modeling arbitrary acquisition trajectories, and creating flexible, end-to-end trainable pipelines through a high-level Python API. Code is available at: https://github.com/csyben/PYRO-NN

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Computed Tomography (CT) is a widely utilized imaging modality in clinical settings. Using densely acquired rotational X-ray arrays, CT can capture 3D spatial features. However, it is confronted with challenged such as significant time consumption and high radiation exposure. CT reconstruction methods based on sparse-view X-ray images have garnered substantial attention from researchers as they present a means to mitigate costs and risks. In recent years, diffusion models, particularly the Latent Diffusion Model (LDM), have demonstrated promising potential in the domain of 3D CT reconstruction. Nonetheless, due to the substantial differences between the 2D latent representation of X-ray modalities and the 3D latent representation of CT modalities, the vanilla LDM is incapable of achieving effective alignment within the latent space. To address this issue, we propose the Consistent Latent Space Diffusion Model (CLS-DM), which incorporates cross-modal feature contrastive learning to efficiently extract latent 3D information from 2D X-ray images and achieve latent space alignment between modalities. Experimental results indicate that CLS-DM outperforms classical and state-of-the-art generative models in terms of standard voxel-level metrics (PSNR, SSIM) on the LIDC-IDRI and CTSpine1K datasets. This methodology not only aids in enhancing the effectiveness and economic viability of sparse X-ray reconstructed CT but can also be generalized to other cross-modal transformation tasks, such as text-to-image synthesis. We have made our code publicly available at https://anonymous.4open.science/r/CLS-DM-50D6/ to facilitate further research and applications in other domains.