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

Abstract

Iterative and generative denoisers are increasingly used under the assumption that multi-step refinement outperforms a single regression pass. We show the opposite for \emph{label-free} denoising. An \emph{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 \emph{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 \textbf{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.