Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restoration

Xiaohui Sun; Hanlin Wu

cs.CVMar 4, 2026

Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restoration

Authors: Xiaohui Sun, Hanlin Wu

Organizations: School of Information Science and Technology, Beijing Foreign Studies University, Beijing 100089, China

Abstract

Face restoration can be formulated as a continuous-time transformation between image distributions via Flow Matching (FM). However, standard FM typically employs independent coupling, ignoring the statistical correlation between low-quality (LQ) and high-quality (HQ) data. This leads to intersecting trajectories and high velocity-field curvature, requiring multi-step integration. We propose Shortcut-constrained Coupling Flow for Face Restoration (SCFlowFR) to address these challenges. By establishing a data-dependent coupling, we explicitly model the LQ-HQ dependency to minimize path crossovers and promote near-linear probability flow. Furthermore, we employ a conditional mean estimator to refine the source distribution's anchor, effectively tightening the transport cost and stabilizing the velocity field. To ensure stable one-step inference, a shortcut constraint is introduced to supervise average velocities over arbitrary intervals, mitigating discretization bias in large-step updates. SCFlowFR achieves state-of-the-art one-step restoration, providing a superior trade-off between perceptual fidelity and computational efficiency.

Figures & tables

Fig. 1: (a) Intersecting paths in independent coupling. (b) Resulting curved velocity field in vanilla FM. (c) Straighter trajectories via data-dependent coupling. (d) One-step sampling via shortcut-constrained average velocity.

Fig. 2: Overview of SCFlowFR. We construct a coupled LQ–HQ transport path (left), conditioning the velocity field $\bm{v_{\theta}}$ on a coarse estimate $\bm{c}$ from $\tau_{\phi}$ . A shortcut constraint then enables average velocity prediction over time interval $\Delta t$ .

Type	Method	Steps	Efficiency		Quality Metrics
Type	Method	Steps	Params (M) $\downarrow$	FPS $\uparrow$	FID $\downarrow$	PSNR (dB) $\uparrow$	LPIPS $\downarrow$	MUSIQ $\uparrow$	BRISQUE $\downarrow$
Multi-step	DiffBIR [ 15 ]	50	1667	0.11	16.91	24.15	0.30	76.05	-1.09
	StableSR [ 7 ]	30	1410	5.80	16.96	24.33	0.27	71.56	20.64
	PMRF [ 17 ]	25	183	2.85	21.70	23.59	0.31	61.79	24.49
	FlowIE [ 11 ]	5	1717	1.17	17.10	23.45	0.27	73.38	2.28
One-step	DMDNet [ 18 ]	1	40	8.40	29.85	24.09	0.30	69.76	19.26

TABLE I: Quantitative results on the CelebA-Test dataset. Among all one-step methods, best in red , second-best in blue .

Fig. 3: Qualitative comparisons on the CelebA-Test dataset.

Method	LFW		CelebChild		WebPhoto
Method	NIQE $\downarrow$	BR. $\downarrow$	NIQE $\downarrow$	BR. $\downarrow$	NIQE $\downarrow$	BR. $\downarrow$
StableSR [ 7 ]	5.24	-0.22	4.91	3.23	5.78	2.02
DiffBIR [ 15 ]	5.68	-3.09	5.48	1.40	6.01	4.58
OSEDiff [ 20 ]	4.72	2.78	5.07	9.82	5.26	5.89
FlowIE [ 11 ]	4.27	1.16	4.44	7.39	4.80	6.83
SCFlowFR	4.11	-1.01	4.25	3.23	4.38	2.89

TABLE II: No-reference metrics on three wild datasets. Best in red , second-best in blue . “BR.” denotes BRISQUE.

Method	Steps	FID $\downarrow$	PSNR(dB) $\uparrow$	BRISQUE $\downarrow$
Model-w/o- $\mathcal{L}_{\text{SC}}$	1	287.23	20.85	51.22
Model-w/- $\mathcal{L}_{\text{consis}}$	5	18.54	24.04	3.17
Model-w/o-cond	1	19.01	23.08	1.55
Ours	1	16.36	24.25	0.90

TABLE III: Ablation studies on the CelebA-Test dataset. Best performance is highlighted in red .

Fig. 4: Qualitative comparisons on three wild datasets. From top to bottom: samples from the CelebChild, LFW, and WebPhoto datasets, respectively.

Image Restoration

Image restoration uses computational methods to recover useful visual content from noisy, blurred, low-resolution, or otherwise degraded images.

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Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.

Abstract

Image Restoration

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