Noise2Flow: single-image conditional mean denoising flows from weak-anchor couplings

PurposeSingle-image denoising is needed when clean targets and repeated acquisitions are unavailable, as in low-dose computed tomography (CT) and fluorescence microscopy. Existing per-image methods often assume pixel-wise noise independence, which fails under spatially correlated noise, and imperfect single-image denoisers commonly leave residual noise. We learn a proxy mean-velocity direction field from one noisy image so that a single transport step exceeds the imperfect anchors used as supervision.ApproachNoise2Flow runs weak single-image denoisers on the noisy image to form source–target couplings. The displacement from input to anchor is a directional proxy for the mean restoration velocity. For each imposed linear segment, MeanFlow’s finite-interval average velocity reduces exactly to a constant secant. A flow network is trained with a direction-normalized objective that regularizes predictions at states in a stochastic tube around the noisy-to-anchor segment toward a common secant direction. At inference, the weak denoisers are discarded; one update with a calibrated transport budget restores the image.ResultsOn the fluorescence microscopy denoising (FMD) test set of 48 images, Noise2Flow reaches 34.91 dB peak signal-to-noise ratio and 0.887 structural similarity, 0.52 dB above Filter2Noise, and 1.00 dB above Noise2Detail. On 1311 low-dose CT slices from 10 Mayo Clinic patients, it reaches 28.82 dB and 0.714, 0.91 dB above Filter2Noise and 1.23 dB above Noise2Detail. One-step inference is within 0.11 dB of 10-step Heun; tube sampling improves the 10-step Heun result relative to on-segment training; a calibrated extrapolation factor moves the flow past residual-noise anchors of varying quality.ConclusionsA proxy mean-velocity direction field can be learned from a single noisy medical image by treating weak-denoiser outputs as directional anchors rather than final targets. The straight proxy path defines the one-step endpoint update; tube regularization and calibrated extrapolation carry that update past residual-noise anchors. The learned flow exceeds residual-noise anchors and supports reference-free restoration in data-limited imaging.