# One-Step Is Optimal: Unconditional Rectified Flows are Noise2Noise Denoisers, and Multi-Step Integration Provably Hurts---A Benchmark and Task-Based Detectability Study on Low-Dose CT

arXiv: https://arxiv.org/abs/2609.31670 · HTML: https://mlsanity.com/paper/2609.31670/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [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)
- [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)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [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)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (2022)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [Zero-Shot Noise2Noise: Efficient Image Denoising without any Data](https://mlsanity.com/paper/2303.11253/) (2023)
- [CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization](https://mlsanity.com/paper/2304.01814/) (2023)
- [Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration](https://mlsanity.com/paper/2410.00418/) (2024)
- [Hallucination Index: An Image Quality Metric for Generative Reconstruction Models](https://mlsanity.com/paper/2407.12780/) (2024)
- [Assessing the Impact of Deep Neural Network-based Image Denoising on Binary Signal Detection Tasks](https://mlsanity.com/paper/2104.14037/) (2021)
- [A study of why we need to reassess full reference image quality assessment with medical images](https://mlsanity.com/paper/2405.19097/) (2024)
- [WIA-LD2ND: Wavelet-based Image Alignment for Self-supervised Low-Dose CT Denoising](https://mlsanity.com/paper/2403.11672/) (2024)
- [The Generation Phases of Flow Matching: a Denoising Perspective](https://mlsanity.com/paper/2510.24830/) (2025)
- [PFCM: Poisson flow consistency models for low-dose CT image denoising](https://mlsanity.com/paper/2402.08159/) (2024)
- [Assessing the performance of CT image denoisers using Laguerre-Gauss Channelized Hotelling Observer for lesion detection](https://mlsanity.com/paper/2412.02920/) (2024)

## Abstract (arXiv)

Iterative and generative denoisers are increasingly used under the assumption that multi-step refinement outperforms a single regression pass. We show the opposite for label-free denoising. An unconditional rectified flow trained on two noisy observations of the same signal, as in Noise2Noise, has a minimiser whose one-step readout is exactly the MMSE denoiser without requiring clean targets. In contrast, multi-step integration provably departs from the MMSE solution because the flow terminates at the noisy data distribution rather than the clean-signal distribution. This departure is exact in a tractable Gaussian model and is confirmed experimentally: one-step flow matches a direct regressor, whereas multi-step Euler integration progressively reduces fidelity. Counterintuitively, the degradation increases with training quality, as a better velocity field more faithfully transports samples toward the noisy terminal law. The key ingredient is therefore the decorrelated pairing, not the flow machinery: a one-step regressor trained on matched noisy pairs gives our best label-free result (+1.99,dB). We evaluate these findings on CTDenoiser, a controlled low-dose CT benchmark spanning five architectures and supervised, similarity-based, blind-spot, and per-image methods. Among label-free approaches, only correlated-noise-aware Noise2Sim improves over the noisy baseline, while Noise2Void is flat-to-negative because CT noise violates its pixel-independence assumption. Finally, although supervised denoisers gain approximately 4,dB PSNR, a channelized Hotelling observer shows reduced low-contrast lesion detectability, revealing clinically relevant degradation missed by PSNR and SSIM.