单步即最优：无条件整流流是 Noise2Noise 去噪器，多步积分确有损害——低剂量 CT 上的基准与基于任务的检测性研究
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
AI总结：
本研究证明在无标签去噪中，无条件整流流的一步读出即达 MMSE 最优，多步积分反而降低保真度；通过低剂量 CT 基准 CTDenoiser 验证，并揭示 PSNR 提升掩盖了临床检测能力的下降。
AI中文摘要：
迭代式和生成式去噪器在“多步细化优于单次回归”的假设下被越来越多地使用。我们针对无标签去噪展示了相反的结果。一个在同一个信号的两个噪声观测上训练的无条件整流流（如 Noise2Noise 中那样），其最小化器的一步读出恰好是 MMSE 去噪器，且无需干净目标。相比之下，多步积分被证明会偏离 MMSE 解，因为流终止于噪声数据分布而非干净信号分布。这种偏离在一个可解析的高斯模型中精确成立，并通过实验得到证实：一步流与直接回归器匹配，而多步欧拉积分则逐步降低保真度。反直觉的是，退化随训练质量的提高而加剧，因为更好的速度场会更忠实地将样本输送到噪声终态分布。因此，关键要素是去相关的配对，而非流机制本身：在匹配的噪声对上训练的一步回归器给出了我们最佳的无标签结果（+1.99 dB）。我们在 CTDenoiser 上评估了这些发现，这是一个受控的低剂量 CT 基准，涵盖五种架构以及监督式、基于相似性、盲点和逐图像方法。在无标签方法中，只有感知相关噪声的 Noise2Sim 比噪声基线有所改进，而 Noise2Void 持平甚至为负，因为 CT 噪声违反了其像素独立性假设。最后，尽管监督式去噪器获得了约 4 dB 的 PSNR 提升，但通道化 Hotelling 观测器显示低对比度病变检测能力下降，揭示了 PSNR 和 SSIM 未能捕捉到的临床相关退化。
英文摘要：
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.
