# RelativeFlow: Taming Medical Image Denoising Learning with Noisy Reference

arXiv: https://arxiv.org/abs/2604.15459 · HTML: https://mlsanity.com/paper/2604.15459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Toward Convolutional Blind Denoising of Real Photographs](https://mlsanity.com/paper/1807.04686/) (2018)
- [MemNet: A Persistent Memory Network for Image Restoration](https://mlsanity.com/paper/1708.02209/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Variational Denoising Network: Toward Blind Noise Modeling and Removal](https://mlsanity.com/paper/1908.11314/) (2019)
- [MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusion](https://mlsanity.com/paper/2203.12621/) (2022)
- [CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization](https://mlsanity.com/paper/2304.01814/) (2023)
- [GRDN:Grouped Residual Dense Network for Real Image Denoising and GAN-based Real-world Noise Modeling](https://mlsanity.com/paper/1905.11172/) (2019)
- [Patch2Self: Denoising Diffusion MRI with Self-Supervised Learning](https://mlsanity.com/paper/2011.01355/) (2020)
- [SDnDTI: Self-supervised deep learning-based denoising for diffusion tensor MRI](https://mlsanity.com/paper/2111.07220/) (2021)
- [Deformed2Self: Self-Supervised Denoising for Dynamic Medical Imaging](https://mlsanity.com/paper/2106.12175/) (2021)
- [CFNet: Conditional Filter Learning with Dynamic Noise Estimation for Real Image Denoising](https://mlsanity.com/paper/2211.14576/) (2022)
- [Calibrating Data Mismatches in Deep Learning-Based Quantitative Ultrasound Using Setting Transfer Functions](https://mlsanity.com/paper/2210.01958/) (2022)

## Abstract (arXiv)

Medical image denoising (MID) lacks absolutely clean images for supervision, leading to a noisy reference problem that fundamentally limits denoising performance. Existing simulated-supervised discriminative learning (SimSDL) and simulated-supervised generative learning (SimSGL) treat noisy references as clean targets, causing suboptimal convergence or reference-biased learning, while self-supervised learning (SSL) imposes restrictive noise assumptions that are seldom satisfied in realistic MID scenarios. We propose RelativeFlow, a flow matching framework that learns from heterogeneous noisy references and drives inputs from arbitrary quality levels toward a unified high-quality target. RelativeFlow reformulates flow matching by decomposing the absolute noise-to-clean mapping into relative noisier-to-noisy mappings, and realizes this formulation through two key components: 1) consistent transport (CoT), a displacement map that constrains relative flows to be components of and progressively compose a unified absolute flow, and 2) simulation-based velocity field (SVF), which constructs a learnable velocity field using modality-specific degradation operators to support different medical imaging modalities. Extensive experiments on Computed Tomography (CT) and Magnetic Resonance (MR) denoising demonstrate that RelativeFlow significantly outperforms existing methods, taming MID with noisy references.