# Poisson Flow Consistency Training

arXiv: https://arxiv.org/abs/2510.21857 · HTML: https://mlsanity.com/paper/2510.21857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [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)
- [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)
- [DU-GAN: Generative Adversarial Networks with Dual-Domain U-Net Based Discriminators for Low-Dose CT Denoising](https://mlsanity.com/paper/2108.10772/) (2021)
- [Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising](https://mlsanity.com/paper/1901.05593/) (2019)
- [Full-band General Audio Synthesis with Score-based Diffusion](https://mlsanity.com/paper/2210.14661/) (2022)
- [PFCM: Poisson flow consistency models for low-dose CT image denoising](https://mlsanity.com/paper/2402.08159/) (2024)
- [High Noise Scheduling is a Must](https://mlsanity.com/paper/2404.06353/) (2024)
- [Enhancing Low Dose Computed Tomography Images Using Consistency Training Techniques](https://mlsanity.com/paper/2411.12181/) (2024)

## Abstract (arXiv)

The Poisson Flow Consistency Model (PFCM) is a consistency-style model based on the robust Poisson Flow Generative Model++ (PFGM++) which has achieved success in unconditional image generation and CT image denoising. Yet the PFCM can only be trained in distillation which limits the potential of the PFCM in many data modalities. The objective of this research was to create a method to train the PFCM in isolation called Poisson Flow Consistency Training (PFCT). The perturbation kernel was leveraged to remove the pretrained PFGM++, and the sinusoidal discretization schedule and Beta noise distribution were introduced in order to facilitate adaptability and improve sample quality. The model was applied to the task of low dose computed tomography image denoising and improved the low dose image in terms of LPIPS and SSIM. It also displayed similar denoising effectiveness as models like the Consistency Model. PFCT is established as a valid method of training the PFCM from its effectiveness in denoising CT images, showing potential with competitive results to other generative models. Further study is needed in the precise optimization of PFCT and in its applicability to other generative modeling tasks. The framework of PFCT creates more flexibility for the ways in which a PFCM can be created and can be applied to the field of generative modeling.