Count-aware diffusion with autoregressive inference for low-count PET reconstruction enhancement

Low-count positron emission tomography (PET) reduces injected activity or acquisition time, but fewer detected coincidence events compromise image quality and quantitative reliability. Existing diffusion-based PET enhancement methods commonly use generic, count-agnostic Gaussian schedules that do not explicitly represent acquisition/count-dependent variation in degradation severity between paired standard- and low-count reconstructions. Direct incorporation of multi-step history may also complicate Markovian reverse inference. We propose a count-informed, endpoint-conditioned diffusion bridge in the reconstructed-image domain with gated autoregressive inference (GAI). The bridge is anchored to paired reconstructed endpoints: its conditional mean follows the standard-to-low-count residual, while a normalized expected-count trajectory controls progression along that residual and the aggregate latent variance. Measurement-level Poisson counting statistics motivate this trajectory from acquisition duration or injected-activity ratio, but no Poisson likelihood is imposed on reconstructed PET voxels. During reverse inference, GAI summarizes previous reverse states within an augmented state that retains a first-order Markov formulation and permits closed-form, count-conditioned updates. We evaluated the method on four-center total-body [¹⁸F]FDG short-duration PET datasets and a simulated BrainWeb low-dose dataset. On the Shanghai Ruijin cohort, it increased PSNR by 5.33 dB and SSIM by 0.043 and reduced RMSE by 53.4% for 3s acquisitions relative to the unenhanced short-duration PET (sdPET) input. At 1s, PSNR increased by 5.91 dB and RMSE decreased by more than 60%. BrainWeb provided proof-of-concept evidence under controlled count reduction. These results support count-informed degradation modeling for low-count PET enhancement in the reconstructed-image domain.