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

2026-07-28

AI Summary

This work addresses the challenge of learning unbiased generative models from noisy training data in scientific imaging scenarios where clean references are unavailable. The authors propose NR-CFM, a method built upon the conditional flow matching (CFM) framework that recovers the clean data distribution using only a single noisy observation per sample. NR-CFM introduces a novel closed-form clean endpoint correction mechanism tailored for additive white Gaussian noise and extends to arbitrary Gaussian noise covariance structures via a data-driven strategy—all without requiring any clean samples during training. Experimental results demonstrate that NR-CFM outperforms NR-GAN across various noise settings, generates plausible particle images even at extremely low signal-to-noise ratios (as low as 0.001), matches the performance of Ambient Diffusion, and enables both efficient sampling and stable training.

Abstract

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.

Problem

• noise-robust generation
• noisy datasets
• clean sample generation
• scientific imaging
• additive noise

Innovation

• Noise-Robust Conditional Flow Matching
• Generative Modeling
• Noisy Data Learning
• Gaussian Noise Correction
• Scientific Imaging