EPC-RawDC: Equivariant Physics Constrained 3D Diffusion with Raw Data Consistency for CBCT to CT Image Synthesis

Cone beam computed tomography (CBCT) is widely used for image guided and adaptive radiotherapy, but scatter, noise, reconstruction artifacts, and inaccurate Hounsfield units limit its quantitative use. Recent diffusion approaches for CBCT to CT synthesis remain largely image driven, with limited use of the underlying acquisition physics. We propose EPC-RawDC, a conditional 3D latent diffusion framework that combines volumetric generative modeling with two complementary constraints derived from the same scanner specific CBCT forward model. First, geometry equivariant projection constraint exploits the rotational equivariance of the CBCT forward operator by supervising the synthesized CT through correspondingly transformed reference projections. Second, raw data consistency uses noisy projection measurements of the individual acquisition as scan specific supervision during training. The framework was evaluated on two independent clinical cohorts with distinct scanner geometries and projection sources. For JUST, the physics constraints used measured clinical raw CBCT projections acquired with an Elekta system, whereas for SynthRAD2025 the projection data were simulated from the reference CT using a Varian geometry with Poisson photon statistics. EPC-RawDC achieved an SSIM of 0.97 in both cohorts and improved PSNR over DDPM by 2.66 dB on SynthRAD2025 and 2.10 dB on JUST, while reducing mean MAE by 20.3% and 19.0%, respectively. On SynthRAD2025, projection consistency and equivariant errors were reduced by 55.0% and 41.4% relative to DDPM. These results demonstrate that combining a volumetric diffusion prior with scanner geometry and scan specific projection measurements improves quantitative CBCT to CT synthesis across both simulated and measured projection domains. Code available after publication at https://github.com/ALZAHRAALTALIB/EPC-RawDC.