Beyond Fixed Inference: Quantitative Flow Matching for Adaptive Image Denoising

Jigang Duan; Genwei Ma; Xu Jiang; Wenfeng Xu; Ping Yang; Xing Zhao

cs.CVApr 2, 2026

Beyond Fixed Inference: Quantitative Flow Matching for Adaptive Image Denoising

Authors: Jigang Duan, Genwei Ma, Xu Jiang, Wenfeng Xu, Ping Yang, Xing Zhao

Organizations: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · National Center for Applied Mathematics Beijing, Capital Normal University and Academy for multidisciplinary studies, Capital Normal University, Beijing, 100048, China · Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

Abstract

Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent across different noise levels, leading to degraded restoration quality under mismatch between training and inference. To address this issue, we propose a quantitative flow matching framework for adaptive image denoising. The method first estimates the input noise level from local pixel statistics, and then uses this quantitative estimate to adapt the inference trajectory, including the starting point, the number of integration steps, and the step-size schedule. In this way, the denoising process is better aligned with the actual corruption level of each input, reducing unnecessary computation for lightly corrupted images while providing sufficient refinement for heavily degraded ones. By coupling quantitative noise estimation with noise-adaptive flow inference, the proposed method improves both restoration accuracy and inference efficiency. Extensive experiments on natural, medical, and microscopy images demonstrate its robustness and strong generalization across diverse noise levels and imaging conditions.

Figures & tables

Fig. 1: Qualitative denoising results of the proposed method under different Gaussian noise levels. For each example, the left image is the noisy input and the right image is the corresponding denoised result. The noise standard deviation $\sigma$ is shown in the upper-left corner of each noisy image. (a)–(c) correspond to medium-, high-, and very high-noise conditions, respectively.

Fig. 2: Conceptual comparison of denoising mechanisms under different noise conditions. (a) Traditional network-based model. (b) Flow-based generative model with a fixed inference trajectory. (c) Conditional flow matching model guided by the noisy observation. (d) Ideal noise-aware model with trajectories better matched to different noise levels. Here,

x_{0}

denotes the clean image,

x_{T}

denotes the noisy initial state, and

x_{1}

x_{2}

, and

x_{3}

represent inputs under high-, medium-, and low-noise conditions, respectively.

Fig. 3: Overview of the proposed method. (a) Overall pipeline, including noise-level estimation, computation of the adaptive starting time and inference grid, and reverse flow integration for denoising. (b) Intermediate denoising results at different time points during adaptive inference.

Fig. 4: Pipeline of the proposed quantitative noise estimation method. (a) Illustration of block-wise pixel differences in noise-free and noisy images after partitioning into non-overlapping $2\times 2$ patches. (b) Estimation of the global noise level using range and middle-range statistics, followed by calibration, random fusion, and sample averaging.

Fig. 5: Qualitative denoising comparisons on the BSDS 500 dataset. From left to right: noisy input, supervised baseline DVT [ 60 ] , self-supervised baseline MASH [ 23 ] , flow-based baseline DeltaFM [ 37 ] , conditional flow-matching baseline CE-CFM [ 41 ] , the proposed method, and the ground-truth reference. From top to bottom, the Gaussian noise standard deviations are 0.22, 0.51, 0.61, and 1.00, respectively. The PSNR/SSIM values for each result are shown below the corresponding image.

Fig. 6: Qualitative comparison of restored ROIs under different noise levels. In each subfigure, the leftmost image shows the noisy input, where the red box indicates the selected ROI, and the remaining images show the corresponding magnified ROIs restored by different methods. (a) Low-noise case. (b) High-noise case. PSNR/SSIM values are reported below each result.

Method	Venue	Overall splits						Test subsets by noise level
		Train		Validation		Test		Medium noise		High noise		Very high noise
		PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
Noisy input	–	7.7660	0.0847	7.5475	0.0895	6.8602	0.0738	22.7474	0.5974	16.6710	0.3773	5.0450	0.0158
DVT	ECCV 2024	21.1297	0.5491	21.2101	0.5483	20.9563	0.5419	24.6206	0.7986	23.7915	0.7523	20.4850	0.5078
MASH	CVPR 2024	20.1750	0.5025	20.2312	0.5149	19.9320	0.5279	25.7219	0.8232	24.7795	0.7642	19.1535	0.4892
DeltaFM	ICCV 2025	15.1461	0.2522	15.2940	0.2547	14.5999	0.2296	26.8789	0.8573	27.2161	0.8193	12.7341	0.1393

TABLE I: Comparison of PSNR (dB) and SSIM for different methods on the training, validation, and test sets. The medium-, high-, and very-high-noise results are obtained by further partitioning the test set according to the noise level.

Fig. 7: Qualitative comparison on the FMDD dataset. From left to right: noisy input, supervised baseline TransUNet [ 65 ] , flow-based baseline MOTFM [ 66 ] , conditional flow-based baseline FlowSDF [ 67 ] , QFM (Ours), and the reference image. The second and fourth rows show enlarged ROI patches corresponding to the red boxes in the first and third rows, respectively. PSNR/SSIM values are reported below each result.

Method	Venue	Raw		Avg2		Avg4		Avg8		Avg16
Method	Venue	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
Noisy Image	–	27.9524	0.5735	30.8260	0.7003	33.6758	0.8114	36.6080	0.8947	40.1838	0.9501
TransUNet	MIA 2024	34.7428	0.8983	35.5516	0.9123	36.0403	0.9192	36.4022	0.9228	36.8469	0.9249
MOTFM	MICCAI 2025	31.9868	0.7528	34.7947	0.8546	37.1023	0.9160	39.0293	0.9489	41.0715	0.9661
FlowSDF	IJCV 2025	31.9759	0.7788	33.4901	0.8529	34.1086	0.8835	34.3907	0.8973	34.6921	0.9054
QFM	Ours	35.0272	0.9040	36.5377	0.9264	38.0481	0.9444	39.6858	0.9595	41.9457	0.9721

TABLE II: Quantitative comparison of denoising performance on the FMDD dataset. Raw denotes the original noisy input, while Avg2, Avg4, Avg8, and Avg16 denote images obtained by averaging 2, 4, 8, and 16 frames, respectively.

Fig. 8: Qualitative comparison on the Mayo dataset. From left to right: FBP, SIRT, TransUNet, MOTFM, FlowSDF, QFM (Ours), and the reference image. The second and fourth rows show enlarged ROI patches corresponding to the red boxes in the first and third rows, respectively. Display windows are set to [-1000 HU, 1450 HU] for the full images and [-1000 HU, 630 HU] for the ROI patches. PSNR/SSIM values are reported below each result.

Anatomical Region	Number of Images	Metric	Noisy Image	TransUNet	MOTFM	FlowSDF	QFM (Ours)
Chest	1047	PSNR	28.7306	42.7329	40.7846	42.9543	44.2525
Chest	1047	SSIM	0.4577	0.9505	0.9416	0.9477	0.9649
Abdomen	1205	PSNR	27.7540	41.8156	39.1901	42.8373	44.0748
Abdomen	1205	SSIM	0.4428	0.9476	0.9402	0.9493	0.9591

TABLE III: Quantitative comparison of denoising performance on the Mayo dataset.

Fig. 9: Qualitative comparison of ablation results under different noise conditions. From left to right: noisy input, the variant without quantitative noise estimation, QFM (Ours), and the reference image. (a) Low-noise condition. (b) Medium-noise condition. (c) High-noise condition.

Fig. 10: Quantitative comparison of the ablation study under different noise intensities. Compared with the variant without quantitative noise estimation, QFM consistently improves both PSNR and SSIM, with the largest gains observed under high-noise conditions.

Fig. 11: Visualization of the progressive denoising process under different noise levels. Different input noise intensities lead to different effective reverse trajectories and different numbers of denoising steps. (a) Low-noise case with $\sigma=0.31$ . (b) High-noise case with $\sigma=0.67$ .

Image Denoising

Image denoising removes unwanted noise while preserving the edges, textures, and colors needed for faithful images.

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IR-Flow: Bridging Discriminative and Generative Image Restoration via Rectified Flow

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In image restoration, single-step discriminative mappings often lack fine details via expectation learning, whereas generative paradigms suffer from inefficient multi-step sampling and noise-residual coupling. To address this dilemma, we propose IR-Flow, a novel image restoration method based on Rectified Flow that serves as a unified framework bridging the gap between discriminative and generative paradigms. Specifically, we first construct multilevel data distribution flows, which expand the ability of models to learn from and adapt to various levels of degradation. Subsequently, cumulative velocity fields are proposed to learn transport trajectories across varying degradation levels, guiding intermediate states toward the clean target, while a multi-step consistency constraint is presented to enforce trajectory coherence and boost few-step restoration performance. We show that directly establishing a linear transport flow between degraded and clean image domains not only enables fast inference but also improves adaptability to out-of-distribution degradations. Extensive evaluations on deraining, denoising and raindrop removal tasks demonstrate that IR-Flow achieves competitive quantitative results with only a few sampling steps, offering an efficient and flexible framework that maintains an excellent distortion-perception balance. Our code is available at https://github.com/fanzh03/IR-Flow.

Abstract

Image Denoising

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