EPC-3D-Diff: Equivariant Physics Consistent Conditional 3D Latent Diffusion for CBCT to CT Synthesis

Cone-beam CT (CBCT) is routinely acquired during radiotherapy for patient setup, but its quantitative reliability is degraded by scatter, noise, and reconstruction artifacts, limiting Hounsfield Unit (HU) accuracy. We propose EPC-3D-Diff, a novel conditional 3D latent diffusion framework for volumetric CBCT to CT synthesis that introduces a projection domain equivariance loss derived from acquisition physics. Unlike common image domain equivariance, we exploit the fact that an in plane rotation of the volume corresponds to an angular shift in its projections. During training, we enforce this relationship by forward projecting rotated synthesized CT volumes and matching them to appropriately angle shifted projections of the paired target CT, yielding a physics consistent equivariance constraint integrated into the diffusion objective. To capture full 3D context efficiently, conditional diffusion is performed in a compact latent space learnt by a lightweight 3D autoencoder, preserving axial depth while downsampling in plane resolution for stable training. We validate on a paired head CBCT/CT phantom dataset, including repeat scans, and paired clinical data using patient wise splits, and perform single and mixed domain training, ablations, and comparisons with diffusion and CycleGAN. EPC-3D-Diff generalizes well and achieved substantial improvements, +7.4 dB (phantom) and +1.8 dB (clinical data) in PSNR compared to state of the art methods, alongside improved SSIM and HU accuracy, within tissue boundaries. Overall, EPC-3D-Diff improves robustness and physics consistency, supporting HU aware synthesis for downstream radiotherapy workflows.

EqDiff-CT: Equivariant Conditional Diffusion model for CT Image Synthesis from CBCT

Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy (IGRT). It provides real time visualization at low cost and dose. However, photon scattering and beam hindrance cause artifacts in CBCT. These include inaccurate Hounsfield Units (HU), reducing reliability for dose calculation, and adaptive planning. By contrast, computed tomography (CT) offers better image quality and accurate HU calibration but is usually acquired offline and fails to capture intra-treatment anatomical changes. Thus, accurate CBCT-to-CT synthesis is needed to close the imaging-quality gap in adaptive radiotherapy workflows. To cater to this, we propose a novel diffusion-based conditional generative model, coined EqDiff-CT, to synthesize high-quality CT images from CBCT. EqDiff-CT employs a denoising diffusion probabilistic model (DDPM) to iteratively inject noise and learn latent representations that enable reconstruction of anatomically consistent CT images. A group-equivariant conditional U-Net backbone, implemented with e2cnn steerable layers, enforces rotational equivariance (cyclic C4 symmetry), helping preserve fine structural details while minimizing noise and artifacts. The system was trained and validated on the SynthRAD2025 dataset, comprising CBCT-CT scans across multiple head-and-neck anatomical sites, and we compared it with advanced methods such as CycleGAN and DDPM. EqDiff-CT provided substantial gains in structural fidelity, HU accuracy and quantitative metrics. Visual findings further confirm the improved recovery, sharper soft tissue boundaries, and realistic bone reconstructions. The findings suggest that the diffusion model has offered a robust and generalizable framework for CBCT improvements. The proposed solution helps in improving the image quality as well as the clinical confidence in the CBCT-guided treatment planning and dose calculations.