# PPFM: Image denoising in photon-counting CT using single-step posterior sampling Poisson flow generative models

arXiv: https://arxiv.org/abs/2312.09754 · HTML: https://mlsanity.com/paper/2312.09754/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 28 of its 69 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [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)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [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)
- [CTformer: Convolution-free Token2Token Dilated Vision Transformer for Low-dose CT Denoising](https://mlsanity.com/paper/2202.13517/) (2022)
- [TransCT: Dual-path Transformer for Low Dose Computed Tomography](https://mlsanity.com/paper/2103.00634/) (2021)
- [Diffusion Probabilistic Priors for Zero-Shot Low-Dose CT Image Denoising](https://mlsanity.com/paper/2305.15887/) (2023)
- [Low-Dose CT Denoising via Sinogram Inner-Structure Transformer](https://mlsanity.com/paper/2204.03163/) (2022)
- [Systematic Review on Learning-based Spectral CT](https://mlsanity.com/paper/2304.07588/) (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)

## Built on by (most cited first, 4 of 4)

- [PFCM: Poisson flow consistency models for low-dose CT image denoising](https://mlsanity.com/paper/2402.08159/) (2024)
- [LangMamba: A Language-driven Mamba Framework for Low-dose CT Denoising with Vision-language Models](https://mlsanity.com/paper/2507.06140/) (2025)
- [MRI-to-CT synthesis using drifting models](https://mlsanity.com/paper/2603.28498/) (2026)
- [ResPF: Residual Poisson Flow for Efficient and Physically Consistent Sparse-View CT Reconstruction](https://mlsanity.com/paper/2506.06400/) (2025)

## Abstract (arXiv)

Diffusion and Poisson flow models have shown impressive performance in a wide range of generative tasks, including low-dose CT image denoising. However, one limitation in general, and for clinical applications in particular, is slow sampling. Due to their iterative nature, the number of function evaluations (NFE) required is usually on the order of 10-103, both for conditional and unconditional generation. In this paper, we present posterior sampling Poisson flow generative models (PPFM), a novel image denoising technique for low-dose and photon-counting CT that produces excellent image quality whilst keeping NFE=1. Updating the training and sampling processes of Poisson flow generative models (PFGM)++, we learn a conditional generator which defines a trajectory between the prior noise distribution and the posterior distribution of interest. We additionally hijack and regularize the sampling process to achieve NFE=1. Our results shed light on the benefits of the PFGM++ framework compared to diffusion models. In addition, PPFM is shown to perform favorably compared to current state-of-the-art diffusion-style models with NFE=1, consistency models, as well as popular deep learning and non-deep learning-based image denoising techniques, on clinical low-dose CT images and clinical images from a prototype photon-counting CT system.