CT-Conditioned Diffusion Prior with Physics-Constrained Sampling for PET Super-Resolution

Reconstructing 3D Computed Tomography (CT) images from a few X-ray projections is a highly ill-posed inverse problem due to the loss of volumetric information. We propose PhyDiCT, a training-free framework that integrates a differentiable Physics-based forward model, grounded in the Beer-Lambert law, with a text-conditioned Diffusion as a strong prior to reconstruct 3D lung CT images. We refer to our approach as training-free since the prior model is used without fine-tuning, and our goal is to steer the denoising procedure to generate samples consistent with X-ray observations. We guide the diffusion generation using Split Gibbs sampling to jointly optimize for projection fidelity (reward) and consistency with prior knowledge. Also, we introduce a test-time refinement step that enhances image realism and anatomical coherence. We extensively evaluate our method on publicly available 3D CT datasets using both perceptual and semantic metrics, demonstrating that it surpasses existing plug-and-play diffusion and fully trained reconstruction approaches. Our findings highlight that combining a strong generative prior with the underlying physics of image formation substantially improves reconstruction quality, e.g., 7.5% improvement on SSIM compared to full training methods. Code will be released at https://github.com/batmanlab/PhyDiCT.

Positron emission tomography (PET) provides essential functional information for disease assessment, however reducing injected activity or acquisition time produces low-dose (LD) PET with stronger count dependent noise and less reliable uptake quantification. Diffusion models offer a promising solution for PET denoising by progressively recovering high-dose (HD) PET images from LD inputs. However, LD-to-HD PET denoising is still challenging due to insufficient anatomical guidance, unstable multi-scale feature propagation, and uncertain frequency domain uptake recovery. We propose AnF-DiffPET, an anatomy- and frequency-guided diffusion framework for computed tomography (CT) conditioned LD PET denoising. The framework integrates Anatomical-Frequency Guidance (AFG), Multi-Scale Cross-Transformer Reconstruction (MSCTR), and Frequency-Contrastive Hard Mining (FCHM) to enhance anatomy aware feature modulation and frequency domain consistency during denoising. Experimental results across four PET/CT datasets show that the proposed method improves image fidelity, anatomical consistency, and quantitative fidelity over representative CNN-based, GAN-based, transformer-based, and diffusion-based methods. The code and trained models will be publicly released upon acceptance.

Positron Emission Tomography (PET) provides important metabolic information for tumor detection and staging but remains significantly less accessible than Computed Tomography (CT) due to its high cost, infrastructure requirements, and reliance on injected radioactive tracers. CT-to-PET image translation using generative models aims to address this disparity, yet state-of-the-art diffusion-based methods are limited by the scarcity of paired training data. To overcome this, we propose a domain-adapted latent diffusion framework that transfers natural-image priors using a relatively small dataset of 21,930 paired CT/PET slices, incorporating a signed power transform to resolve extreme intensity sparsity in PET data. Compared to CPDM, a state-ofthe-art baseline for CT-to-PET image translation, our approach yields superior performance in pixel-wise reconstruction and localized tumor fidelity, demonstrating effective transfer of natural-image priors to the medical domain. We further provide a systematic analysis of evaluation metric reliability for sparse PET data, showing that standard full-image metrics can be misleading indicators of translated image quality, and propose background-filtered and mask-restricted metrics as more clinically meaningful alternatives.