PFCM: Poisson flow consistency models for low-dose CT image denoising

X-ray computed tomography (CT) is widely used for medical diagnosis and treatment planning; however, concerns about ionizing radiation exposure drive efforts to optimize image quality at lower doses. This study introduces Poisson Flow Consistency Models (PFCM), a novel family of deep generative models that combines the robustness of PFGM++ with the efficient single-step sampling of consistency models. PFCM are derived by generalizing consistency distillation to PFGM++ through a change-of-variables and an updated noise distribution. As a distilled version of PFGM++, PFCM inherit the ability to trade off robustness for rigidity via the hyperparameter $D \in (0,\infty)$. A fact that we exploit to adapt this novel generative model for the task of low-dose CT image denoising, via a ``task-specific'' sampler that ``hijacks'' the generative process by replacing an intermediate state with the low-dose CT image. While this ``hijacking'' introduces a severe mismatch -- the noise characteristics of low-dose CT images are different from that of intermediate states in the Poisson flow process -- we show that the inherent robustness of PFCM at small $D$ effectively mitigates this issue. The resulting sampler achieves excellent performance in terms of LPIPS, SSIM, and PSNR on the Mayo low-dose CT dataset. By contrast, an analogous sampler based on standard consistency models is found to be significantly less robust under the same conditions, highlighting the importance of a tunable $D$ afforded by our novel framework. To highlight generalizability, we show effective denoising of clinical images from a prototype photon-counting system reconstructed using a sharper kernel and at a range of energy levels.