# Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets

arXiv: https://arxiv.org/abs/2608.00064 · HTML: https://mlsanity.com/paper/2608.00064/

## 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 26 of its 33 references that are in the map.
- First posted on arXiv 28 Jul 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, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data](https://mlsanity.com/paper/2404.10177/) (2024)
- [Training Deep Learning Based Denoisers without Ground Truth Data](https://mlsanity.com/paper/1803.01314/) (2018)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [How much is a noisy image worth? Data Scaling Laws for Ambient Diffusion](https://mlsanity.com/paper/2411.02780/) (2024)
- [Noise Robust Generative Adversarial Networks](https://mlsanity.com/paper/1911.11776/) (2019)
- [CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM](https://mlsanity.com/paper/2408.05526/) (2024)
- [AmbientFlow: Invertible generative models from incomplete, noisy measurements](https://mlsanity.com/paper/2309.04856/) (2023)
- [Stochastic Forward-Backward Deconvolution: Training Diffusion Models with Finite Noisy Datasets](https://mlsanity.com/paper/2502.05446/) (2025)
- [Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants](https://mlsanity.com/paper/2512.10857/) (2025)
- [Inverse Flow and Consistency Models](https://mlsanity.com/paper/2502.11333/) (2025)

## Abstract (arXiv)

Generative models learn the statistical properties of their training data, so high-quality generation depends on clean and representative datasets. In scientific imaging, acquisition often yields noisy measurements, while collecting clean references can be costly, impractical or even unattainable. Training directly on these measurements results in a model that reproduces the corrupted data. This can be circumvented by learning the clean population distribution directly from the noisy data. Conditional flow matching (CFM) combines a simple regression objective with stable training, efficient sampling, and strong image-generation performance, making it a natural framework for this setting. We introduce Noise-Robust Conditional Flow Matching (NR-CFM), an unconditional generator that learns from one corrupted observation per image. NR-CFM provides a closed-form clean endpoint correction for additive white Gaussian noise and learns a data-driven correction for general Gaussian corruptions with more complex covariance structure. Across the evaluated corruption settings, NR-CFM outperforms NR-GAN in most cases and remains competitive with Ambient Diffusion in the high-noise regime. We further evaluate NR-CFM on scientific data at signal-to-noise ratios as low as 0.001, where it generates plausible particle images from severely corrupted measurements.