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

arXiv: https://arxiv.org/abs/2402.08159 · HTML: https://mlsanity.com/paper/2402.08159/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 30 of its 66 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [One weird trick for parallelizing convolutional neural networks](https://mlsanity.com/paper/1404.5997/) (2014)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusion](https://mlsanity.com/paper/2203.12621/) (2022)
- [Can Deep Learning Outperform Modern Commercial CT Image Reconstruction Methods?](https://mlsanity.com/paper/1811.03691/) (2018)
- [DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Models](https://mlsanity.com/paper/2302.03018/) (2023)
- [Diffusion Probabilistic Priors for Zero-Shot Low-Dose CT Image Denoising](https://mlsanity.com/paper/2305.15887/) (2023)
- [Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling](https://mlsanity.com/paper/2307.03992/) (2023)
- [SVNR: Spatially-variant Noise Removal with Denoising Diffusion](https://mlsanity.com/paper/2306.16052/) (2023)
- [JCCS-PFGM: A Novel Circle-Supervision based Poisson Flow Generative Model for Multiphase CECT Progressive Low-Dose Reconstruction with Joint Condition](https://mlsanity.com/paper/2306.07824/) (2023)
- [PPFM: Image denoising in photon-counting CT using single-step posterior sampling Poisson flow generative models](https://mlsanity.com/paper/2312.09754/) (2023)

## Built on by (most cited first, 5 of 5)

- [Overclocking Electrostatic Generative Models](https://mlsanity.com/paper/2509.22454/) (2025)
- [Poisson Flow Consistency Training](https://mlsanity.com/paper/2510.21857/) (2025)
- [Physics-Driven Independent Pair Generation for Iterative Self-Supervised Low-Dose CT Denoising](https://mlsanity.com/paper/2609.02654/) (2026)
- [A deep dictionary network-based foundation model for ultra-low-dose CT denoising](https://mlsanity.com/paper/2609.16031/) (2026)
- [One-Step Is Optimal: Unconditional Rectified Flows are Noise2Noise Denoisers, and Multi-Step Integration Provably Hurts---A Benchmark and Task-Based Detectability Study on Low-Dose CT](https://mlsanity.com/paper/2609.31670/) (2026)

## Abstract (arXiv)

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 ∈ (0,∞). 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.