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Flow Straight to Reality: Perceptually Consistent Flow Matching for Efficient Image Restoration
Sangwoo Jo, Donggeun Ko, Jayeon Kang, Youngsang Kwak, Jaehwa Kwak, Sungjoon Choi
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Summary
The paper introduces PCFlow (Perceptually Consistent Flow Matching), a unified framework for efficient image restoration that balances the distortion-perception tradeoff. It utilizes a Latent Consistency Flow Matching (LCFM) objective for stable, few-step inference and a Latent Consistency Perceptual Loss (LCPL) to ensure semantic alignment. To resolve gradient conflicts between structural and perceptual objectives, it employs a conflict-free gradient projection strategy. The model uses a lightweight, convolution-only backbone, achieving competitive performance in tasks like blind face restoration, super-resolution, and denoising with reduced computational cost.
Entities (14)
Relation Signals (11)
PCFlow → evaluatedon → Blind Face Restoration
confidence 95% · Extensive evaluations across several benchmarks, including blind face restoration
PCFlow → evaluatedon → Super-Resolution
confidence 95% · Extensive evaluations across several benchmarks, including... super-resolution
PCFlow → uses → LCPL
confidence 95% · we introduce a Latent Consistency Perceptual Loss (LCPL), which encourages the trajectory endpoints to align with perceptually sharp, high-density data manifolds
PCFlow → uses → Conflict-Free Gradient Projection
confidence 95% · we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape
PCFlow → uses → LCFM
confidence 95% · By employing a latent consistency flow matching (LCFM) objective, we enforce geometric consistency along the trajectory
LCFM → enables → few-step inference
confidence 90% · enabling image restoration in as few as three inference steps
PCFlow → usesbackbone → Tiny AutoEncoder
confidence 90% · We employ a pretrained Tiny AutoEncoder [20]... The encoder-decoder operates in a 16-channel latent space
LCPL → uses → VGGNet
confidence 85% · we adopt E-LatentLPIPS [12] as an external perceptual objective... f VGG represents a VGG network
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Abstract
Abstract: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.
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- Source: https://arxiv.org/abs/2608.10544v1
- Canonical: https://arxiv.org/abs/2608.10544v1
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Flow Straight to Reality: Perceptually Consistent Flow Matching for Efficient Image Restoration Sangwoo Jo 1 , Donggeun Ko 2 , Jayeon Kang 1 , Youngsang Kwak 2 , Jaehwa Kwak 2 , and Sungjoon Choi 1 1 Korea University, Seoul, South Korea jasonjo97, nature0213, sungjoonc@korea.ac.kr 2 Aim Future, Seoul, South Korea sean.ko, youngsang.kwak, jaehwa.kwak@aimfuture.ai Abstract. Image restoration is fundamentally constrained by the trade- off 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 Consis- tent 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 Con- sistency 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 gradi- ent projection strategy to stabilize the multi-objective optimization land- scape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs. 1 Introduction Image restoration aims to recover a clean image from its degraded observa- tion, constituting a fundamental class of inverse problems in computer vision. Fundamentally, this process is plagued by the inherent ambiguity of degrada- tion: multiple plausible high-quality reconstructions can map to a single cor- rupted input. As established in classical literature [4, 10], this ambiguity forces a strict distortion-perception tradeoff. Methods that minimize distortion error (e.g., MSE) mathematically collapse to the conditional expectation, yielding over-smoothed results. Conversely, approaches optimizing for perceptual real- ism (e.g., FID) hallucinate high-frequency details, improving visual quality but incurring severe structural deviations and high reconstruction error. A principled way to achieve perceptually optimal solutions is posterior sam- pling, which generates samples from the underlying posterior distribution and arXiv:2608.10544v1 [cs.CV] 11 Aug 2026 2S. Jo et al. Fig. 1: Visual Results of PCFlow on the Blind Face Restoration (BFR). PCFlow consistently produces visually faithful and high-quality reconstructions while requiring only a few inference steps (K = 5). thus attains the optimal perceptual index [4, 10]. However, such methods do not minimize distortion and, in expectation, yield an MSE that can be up to twice the minimum achievable error. Recent diffusion and score based restora- tion approaches leverage generative priors to approximate posterior sampling [5, 13, 21, 23, 26, 33]. While these approaches significantly improve perceptual quality, they rely on iterative stochastic sampling and typically require mul- tiple sampling steps, resulting in substantial computational cost at inference time. To circumvent this, recent multi-stage frameworks decompose the prob- lem: they first predict a fidelity-oriented minimum mean-squared error (MMSE) estimate, and subsequently apply heavy generative refinement to recover de- tails [6,16,19,29]. While effective, such two-stage pipelines inherit architectural complexity and still rely on costly generative steps during inference. In this work, we revisit the problem from a different perspective. Instead of performing stochastic posterior sampling or decomposing restoration into mul- tiple stages, we propose PCFlow (Perceptually Consistent Flow Matching), a unified direct transport framework that effectively balances distortion and per- ception. Rather than decomposing the restoration process, we tackle the multi- objective optimization directly within a continuous latent space. At its core, PCFlow parameterizes a direct vector field from the degraded input to the clean target. By employing a latent consistency flow matching (LCFM) objective, we enforce geometric consistency along the trajectory, ef- fectively straightening the integration path and enabling image restoration in as few as three inference steps. However, learning a few-step transport with an L 2 - based objective inherently risks regression to the posterior mean. To mitigate this effect, we introduce a Latent Consistency Perceptual Loss (LCPL), which encour- ages the trajectory endpoints to align with perceptually sharp, high-density data Perceptually Consistent Flow Matching for Efficient Image Restoration3 manifolds. Nevertheless, simply combining these objectives introduces gradient conflicts, particularly at early transport timesteps (low SNR regimes). To stabi- lize this multi-objective optimization, we adopt a conflict-free gradient projection strategy along with an SNR-adaptive schedule, using the perceptual objective as a steering signal while removing structural gradient components that conflict with perceptual optimization. Furthermore, PCFlow employs a lightweight convolution-only model archi- tecture without attention modules, significantly reducing model size and com- putational cost. Combined with our conflict-free consistency training, PCFlow operates at a fraction of traditional computational costs while achieving effective balance on the distortion-perception curve. Our main contributions are summarized as follows: – We propose PCFlow, a unified direct transport framework that integrates perceptual consistency into a latent flow objective, enabling highly efficient few-step image restoration. – We analyze the destructive gradient interference between structural and perceptual objectives, and introduce a conflict-free, SNR-adaptive gradient alignment method to stabilize training. – We adopt a convolution-only architecture that rivals computationally heavy multi-stage diffusion pipelines, significantly reducing parameter count and inference time. – Extensive evaluations across several benchmarks, including blind face restora- tion, super-resolution, denoising, inpainting, and colorization, demonstrate that PCFlow advances the distortion-perception tradeoff frontier. 2 Related Work 2.1 Generative Models for Image Restoration Image restoration has undergone a paradigm shift with the advent of genera- tive modeling. Primary works have formulated the problem through the lens of Bayesian posterior sampling [5,13,21,23,26,33]. By iteratively drawing sam- ples from the posterior p(x|y)∝ p(x)p(y|x) using diffusion priors, these models attain exceptional perceptual quality. Beyond explicit posterior sampling, condi- tional generative frameworks have been also explored [16,32]. Instead of deriving a posterior via likelihood models, these approaches introduce various mechanisms to incorporate degraded images as conditional inputs. Recent works attempt to bridge distortion minimization and perceptual real- ism through a disjointed, two-stage pipeline [6,19]. Motivated by the distortion- perception tradeoff theory [4, 10], they first anchor the generation to the mini- mum mean-squared error (MMSE) estimator, x ∗ = E[x| y],(1) which mathematically guarantees minimal distortion. Subsequently, they must learn an optimal transport from this safe, over-smoothed estimate x ∗ to the tar- get distribution x. To execute this transport, approaches like DOT [1] attempt 4S. Jo et al. to bypass iterative sampling by directly approximating the transport trajectory with a closed-form solution under Gaussian assumptions. Although effective, such two-stage pipelines introduce additional architectural complexity and com- putational cost at inference time. 2.2 Consistency Flow Matching Flow-based generative models [2,17,18] have recently emerged as an alternative class of generative models that learn a continuous vector field v(x,t) transporting samples between two distributions x 0 ∼ π 0 and x 1 ∼ π 1 through an ordinary differential equation (ODE): dx dt = v(x(t),t),(2) In other words, flow-based approaches directly parameterize the transport vector field between distributions, enabling explicit trajectory modeling and efficient inference through numerical ODE integration. To further improve training and inference efficiency, Consistency Flow Match- ing (CFM) [27] introduces a consistency objective that effectively straightens the flow trajectory by aligning predictions across neighboring timesteps. Instead of explicitly modeling the entire probability path, CFM enforces consistency in both trajectory outputs and velocity field, leading to stable training and sup- porting few step inference. While CFM has demonstrated strong performance in unconditional generative modeling, it has primarily been studied in pixel space. Its extension to conditional generative tasks, such as image restoration, as well as to latent representation spaces remains relatively underexplored. 2.3 Perceptual Objective Perceptual objectives have been widely adopted in image restoration to enhance high-frequency details [11, 14, 24, 25, 31]. A common approach is to incorporate feature-based perceptual losses, most notably LPIPS [30], which measures the distance between pretrained VGGNet features [22] extracted from predicted and ground truth images. Such external perceptual losses encourage semantic simi- larity beyond pixel-wise fidelity and have become standard regularizers in image restoration tasks. E-LatentLPIPS [12] extends LPIPS to latent space, where the training objective remains identical but with additional data augmentation to address the suboptimal loss landscape inherent in latent representations. More recently, several works have explored leveraging internal features of generative models themselves for perceptual supervision, instead of relying on external pretrained networks. These methods utilize intermediate features, such as U-Net midblock layer or decoder features, to define self-perceptual losses [3,15]. By aligning intermediate features, such approaches aim to better preserve generative priors and semantic coherence. However, such methods have been developed primarily for image generation, and their extension to restoration settings remains limited. Perceptually Consistent Flow Matching for Efficient Image Restoration5 ℰ !" ℰ #" 풛 ! 풛 " 퐿 !"#$ 퐿 %&%'( =퐿 !"#$ +휆 !")! 퐿 !")! 퐿 #$%# =피 & [푤 ' ' '(" # ||휙 ' *풛 " −휙 ' 풛 " || ) ] 푣 * *풛 " 휙 ! 휙 " 휙 # ... ... 풟 Fig. 2: Overview of PCFlow. Given a degraded image, our proposed PCFlow en- codes it into latentz 0 using the LQ encoder, and learns the latent transport with a flow model v θ . The restored latent prediction ˆ z 1 is then decoded by D to obtain the final output image ˆ x. The training objective combines a latent consistency flow matching loss L LCFM with a latent consistency perceptual loss L LCPL , computed from multi-level decoder featuresφ l L l=1 , yielding the final objective as L total = L LCFM +λ LCPL L LCPL . 3 Method 3.1 Latent Consistency Flow Matching Formulating Latent Transport. Following ELIR [6], we begin by defining a latent consistency flow matching (LCFM) objective that integrates latent flow matching [7] with consistency training [27]. Given a low-quality (LQ) latent z 0 and its corresponding high-quality (HQ) latent z 1 , we parameterize a vector field v θ that governs the latent transport over time t∈ [0, 1]: dz dt = v θ (z(t),t),(3) where we define a linear interpolation path in the latent space: z t = tz 1 + (1− (1− σ min )t)z 0 , t∈ [0, 1].(4) Here, σ min > 0 prevents degeneration at early timesteps and stabilizes transport learning. Given the number of segments K, we partition the time interval [0, 1] into K subintervals i K , i+1 K K−1 i=0 , and let i = ⌊Kt⌋ denote the segment index. The LCFM objective then penalizes discrepancies in both the predicted trajectory endpoints and the velocity fields: L LCFM (θ) = E z 0 ,z 1 ,t ∆f i θ (z t ,z t+∆t ,t) + α∆v i θ (z t ,z t+∆t ,t) ,(5) 6S. Jo et al. where t∼U(0, 1− ∆t) and the penalty terms are defined as: ∆f i θ (z t ,z t+∆t ,t) = f i θ (z t ,t)− sg f i θ (z t+∆t ,t + ∆t) 2 ,(6) ∆v i θ (z t ,z t+∆t ,t) = v i θ (z t ,t)− sg v i θ (z t+∆t ,t + ∆t) 2 ,(7) f i θ (z t ,t) = z t + i + 1 K − t v i θ (z t ,t).(8) Here, v i θ (z t ,t) denotes the predicted vector field within the i-th segment, and f i θ (z t ,t) represents the predicted trajectory output obtained by a single Euler step toward the end of the segment. sg(·) denotes the stop-gradient operator, and α,∆t are set as hyperparameters. Unconditional and Conditional Training. Following PMRF [19], we con- sider both conditional and unconditional flow models for image restoration. For the unconditional flow model, the flow is initialized from the degraded observa- tion, and the transport is defined as: z t = tz 1 + (1− (1− σ min )t)z ∗ 0 , z ∗ 0 = z 0 + σ s ε,(9) where the vector field v θ (z t ,t) learns to transport samples from this initialization toward the clean image distribution. Here, σ s controls the standard deviation of the Gaussian noise that alleviates singular mapping between low and high dimensional manifolds. For comparison, we also consider conditional flow formulation where the vec- tor field learns from the noise distribution conditioned on the degraded input z 0 , formulated as the following: z t = tz 1 + (1− (1− σ min )t)z ∗ 0 , z ∗ 0 ∼N(0,I),(10) where the corresponding velocity field v θ (z t ,t,z 0 ) learns to transport samples from the noise distribution toward the target clean image conditioned on z 0 . 3.2 Latent Consistency Perceptual Loss While LCFM ensures geometric consistency in latent space, such a method does not explicitly enforce perceptual realism. To incorporate semantic alignment, we introduce a Latent Consistency Perceptual Loss (LCPL). External Perceptual Network. Given a predicted latent ˆ z 1 and the ground- truth latent z 1 , we adopt E-LatentLPIPS [12] as an external perceptual ob- jective, where the perceptual distance is computed between the corresponding latent representations by applying differentiable augmentation and measuring feature discrepancies in a pretrained network: L external (z 1 , ˆ z 1 ) = E z 0 ,z 1 ,t,T h ∥f VGG (T (z 1 ))− f VGG (T ( ˆ z 1 ))∥ 2 i , (11) where f VGG represents a VGG network pretrained on ImageNet [8] and BAPPS dataset [30], and T denotes random differentiable augmentations implemented Perceptually Consistent Flow Matching for Efficient Image Restoration7 in E-LatentLPIPS. We separately train VGGNet for 256×256 resolution for our experiments, as the publicly available pretrained model from E-LatentLPIPS is trained on 512× 512 images. Internal Perceptual Network. Although E-LatentLPIPS [12] provides strong perceptual supervision, it relies on an externally pretrained network and may re- quire additional training for dataset-specific tasks. To reduce dependency on ex- ternal modules, we additionally adopt an internal perceptual objective function defined by the model itself [3]. Specifically, let φ l (z) L l=1 denote intermediate decoder features extracted from latent feature z. The internal perceptual loss is then defined as: L internal (z 1 , ˆ z 1 ) = E z 0 ,z 1 ,t " w l L X l=1 ˆ φ l (z 1 )− ˆ φ l ( ˆ z 1 ) 2 # , (12) where ˆ φ l (·) denotes per-channel normalized features andw l L l=1 are weight val- ues assigned to each feature layer. Note that the formulation is similar to LPL loss [3] except that binary map masking is omitted for simplicity. Perceptual Objective for Latent Consistency Training. To incorporate perceptual alignment into consistency learning, we define a Latent Consistency Perceptual Loss (LCPL) that enforces perceptual similarity between adjacent trajectory predictions: L LCPL (θ) = E z 0 ,z 1 ,t L percep f i θ (z t ,t),f i θ (z t+∆t ,t + ∆t) ,(13) where t ∼ U(0, 1− ∆t) and L percep can be instantiated as either L external or L internal . This objective encourages perceptual consistency of the predicted tra- jectory across neighboring timesteps in latent space. Overall Objective. Hence, our final training objective combines flow consis- tency and perceptual consistency as the following: L total (θ) = L LCFM (θ) + λ LCPL L LCPL (θ),(14) where λ LCPL controls the strength of perceptual steering relative to the struc- tural transport objective. 3.3 Improving Objective with Conflict-Free Gradient Alignment Diagnosing Gradient Conflict. We compute the gradients of the latent con- sistency flow matching objective ∇ θ L LCFM and perceptual objective ∇ θ L LCPL defined in Eq. (14). We observe that the gradients between the structural and the perceptual objective are highly noise-level dependent: the two gradients con- flict in low log-SNR regimes but become increasingly aligned in high log-SNR regimes. This indicates that the two objectives induce conflicting descent direc- tions in the parameter space, particularly in early transport stages. However, naively summing the gradients implicitly assumes 8S. Jo et al. Semantic Target Sub-manifold Structure Manifold Distortion Perceptual Index Better quality Less distortion Unattainable Fig. 3: Gradient alignment between reconstruction and perceptual objec- tives. (Left) The reconstruction objective L LCFM promotes structural fidelity, while the perceptual objective L LCPL encourages perceptual realism toward a semantic target sub-manifold. Our gradient alignment method mitigates conflicts between the gradients and produces a balanced update g total . (Right) In the distortion-perception plane, re- lying solely on LCFM (orange) leads to blurry outputs, whereas over-optimizing LCPL (blue) severely deviates from the input structure and introduces artifacts. In contrast, our aligned trajectory (green) incorporates perceptual guidance while mitigating con- flicting structural updates, allowing the model to move closer to the optimal PD limit. ⟨∇ θ L LCFM ,∇ θ L LCPL ⟩≥ 0,(15) which does not hold in practice. When the inner product is negative, the two ob- jectives produce conflicting optimization directions, leading to destructive gra- dient interference and unstable optimization. This motivates our conflict-free gradient update method combined with noise-aware weighting strategy. λ-scheduling. Recognizing that the gradient alignment naturally improves in high SNR regimes (near the clean target), we modulate the perceptual influ- ence dynamically. Instead of a static hyperparameter, we define λ LCPL (t) as a monotonically increasing function of the timestep t. Conceptually, this ensures that the model establishes a robust, conflict-free structural foundation during the noisy early stages, and progressively unleashes the full power of perceptual steering as the generation refines toward reality. Conflict-Free Gradient Update. To resolve this destructive interference, we draw inspiration from multi-task gradient surgery [28] but adapt it as an asym- metric orthogonal projection. While the LCFM objective provides the structural transport signal, the LCPL objective serves as perceptual guidance that steers the transport trajectory toward perceptually realistic regions of the target man- ifold. Therefore, when the two vectors conflict (i.e., ⟨g LCFM ,g LCPL ⟩ < 0), we preserve the perceptual gradient and remove only the component of the struc- tural gradient that conflicts with it. Perceptually Consistent Flow Matching for Efficient Image Restoration9 Denoting the gradients of the two objectives as g LCFM = ∇ θ L LCFM and g LCPL =∇ θ L LCPL , we update the parameters as the following procedure: θ ← θ− η( ̃g LCFM (t) + λ LCPL (t)g LCPL (t)),(16) where ̃g LCFM is defined as the orthogonal component of g LCFM with respect to g LCPL : ̃g LCFM (t) = g LCFM (t)− 1 ⟨g LCFM ,g LCPL ⟩<0 ⟨g LCFM ,g LCPL ⟩ ∥g LCPL ∥ 2 g LCPL .(17) As a result, the perceptual objective remains an effective steering signal through- out training, whereas reconstruction updates are incorporated only when they do not interfere with perceptual optimization. This asymmetric design enables conflict-free multi-objective optimization and leads to improved perceptual restora- tion performance. We further provide an ablation study comparing alternative projection strategies in our supplementary material. 4 Experiments We evaluate PCFlow on the following tasks: blind face restoration (BFR), super- resolution, denoising, inpainting, and colorization. Following previous baselines [6,19], for BFR, models are trained on FFHQ 512× 512 dataset and evaluated on CelebA-Test, LFW-Test and CelebAdult. For the remaining tasks, models are trained on FFHQ 256× 256 dataset and evaluated on CelebA-Test dataset. 4.1 Implementation Details Training. We train PCFlow using a two-stage procedure. Initially, the model fo- cuses solely on reconstruction quality by setting λ LCPL = 0 for the first 250 train- ing epochs. In the second stage, we enable the perceptual objective and continue training for an additional 250 epochs with the proposed SNR-adaptive weighting, encouraging fine-grained details and perceptual realism. We experiment with dif- ferent λ-scheduling strategies and report the best-performing configuration. For consistency training, we follow ELIR setting the number of consistency steps K = 5 for BFR and K = 3 for the remaining tasks, with a fixed time inter- val ∆t = 0.05. We use a batch size of 128 using AdamW optimizer (β 1 = 0.9, β 2 = 0.999) with weight decay 0.02. We use exponential moving average (EMA) with decay rate 0.999 throughout training. Model Architecture. We employ a pretrained Tiny AutoEncoder [20], a light- weight version of Stable Diffusion VAE [9]. The encoder-decoder operates in a 16-channel latent space and contains approximately 2.4M parameters, providing efficient latent representation while maintaining high reconstruction fidelity. We implement convolution-only U-Net architecture from ELIR. The model takes 32 input channels for conditional setting and 16 input channels for unconditional 10S. Jo et al. Table 1: Quantitative results on BFR. Quantitative comparison of PCFlow with baselines on blind face restoration (BFR) task. The best and second-best results are highlighted in bold and underlined , respectively. PCFlow achieves a favorable restora- tion quality with efficient model architecture and fast inference, obtaining state-of-the- art FID and NIQE scores for CelebA-Test, and FID for CelebAdult dataset. Model Efficiency CelebA-TestLFW CelebAdult Perceptual QualityDistortionPerceptual Quality #Params[M]↓ FPS↑ FID↓ NIQE↓ MUSIQ↑ PSNR↑ SSIM↑ LPIPS↓ FID↓FID↓ CodeFormer9427.13 52.23 4.65 75.55 24.77 0.6732 0.3432 54.28 114.34 GFPGAN(v1.3)87.1459.73 45.95 4.4275.2924.60 0.6802 0.3643 49.58 112.31 VQFRv283.4916.97 46.01 4.1774.40 22.85 0.6446 0.3624 52.50 106.83 Difface (K = 100)182.070.78 37.43 4.3768.31 24.44 0.6579 0.4172 47.23 101.11 DiffBIR (K = 50)1666.930.38 46.23 4.2175.27 23.27 0.6379 0.3876 46.03 111.84 ResShift (K = 4)196.706.85 43.60 4.3772.16 25.32 0.6965 0.3435 54.23 109.04 PMRF (K = 25)182.750.57 37.22 4.1270.36 25.85 0.7098 0.3470 49.98 104.44 ELIR (K = 5)37.5233.11 44.64 5.2667.24 25.560.70300.3735 53.19 105.55 PCFlow (Ours)32.0242.6235.89 3.95 70.35 24.44 0.6680 0.3850 50.68 98.85 setting. Note that the overall architecture is identical to ELIR, but without the MMSE estimator module, resulting in reduction of 5.5M parameters. Latent Perceptual Network. For the internal perceptual network, we ex- tract features from the decoder’s intermediate representations, including the mid-block, three upsampling stages, and the final output layer. The contribu- tion of each feature level is weighted according to its spatial resolution, except for the final output layer, i.e., w l ∝ 2 −r l , where r l denotes the resolution level of feature l. The weights are subsequently normalized to sum to one. For the external perceptual network, to compute the perceptual objective within our customized latent space, we separately train the model following the procedure from E-LatentLPIPS. In addition, we adopt batch normalization which empiri- cally demonstrates more stable training compared to group normalization. 4.2 Quantitative Results Blind Face Restoration. Quantitative results on blind face restoration (BFR) are reported in Tab. 1. PCFlow achieves state-of-the-art perceptual quality, ob- taining the best FID and NIQE on CelebA-Test and the best FID on CelebAdult, while requiring only 32M parameters and five sampling steps (K = 5). Com- pared to ELIR, PCFlow uses fewer parameters (32M vs. 37.5M) and achieves 1.29× higher inference speed (42.62 vs. 33.11 FPS), while substantially improv- ing FID (35.89 vs. 44.64) on CelebA-Test. Furthermore, despite being signifi- cantly smaller and faster than diffusion-based baselines such as PMRF (183M parameters, 0.57 FPS), PCFlow outperforms in perceptual quality metrics while delivering over 75× higher throughput. These results demonstrate that PCFlow provides a favorable trade-off between restoration quality and computational ef- ficiency, achieving strong perceptual restoration performance under a practical few-step inference regime. Perceptually Consistent Flow Matching for Efficient Image Restoration11 Table 2: Quantitative results on the remaining restoration tasks. Quantita- tive comparison of PCFlow with baselines ELIR and PMRF. The best and second-best results are highlighted in bold and underlined , respectively. PCFlow consistently out- performs ELIR in FID, despite using only 21M parameters compared to ELIR (27M) and PMRF (176M), demonstrating favorable perceptual quality with efficient model architecture and fast inference. TaskModel Efficiency Perceptual QualityDistortion #Params[M]↓FID↓PSNR↑ SSIM↑ LPIPS↓ Super Resolution PMRF (K = 25)17644.6424.40 0.6708 0.2991 ELIR2749.2523.57 0.6439 0.3299 PCFlow (Ours)2145.5023.38 0.65120.3328 Denoising PMRF (K = 25)17644.3527.92 0.7782 0.2401 ELIR2747.7026.67 0.75210.2619 PCFlow (Ours)2145.4226.26 0.7480 0.2800 Inpainting PMRF (K = 25)17642.8826.19 0.7383 0.2626 ELIR2747.8224.85 0.7105 0.2840 PCFlow (Ours)2145.5024.920.71950.2936 Colorization PMRF (K = 25)17642.6123.47 0.71220.3463 ELIR2751.7223.150.7113 0.3587 PCFlow (Ours)2145.2122.18 0.7499 0.3596 Other Restoration Tasks. We further provide quantitative results for the remaining restoration tasks, including super-resolution, denoising, inpainting, and colorization, in Tab. 2. PCFlow consistently improves over ELIR in FID across all four image restoration tasks. These results challenge the prevailing paradigm that prioritizes explicit posterior mean estimation followed by trans- port refinement. Instead, we show that directly learning the conditional transport from degraded observations, combined with perceptual supervision as a steering signal, is sufficient to achieve superior distortion-perception trade-offs under a few-step regime. Notably, the improvements are consistent across diverse degra- dation types, suggesting that the proposed formulation generalizes well beyond a specific restoration setting. 4.3 Qualitative Results Blind Face Restoration. Fig. 1 presents qualitative comparisons on blind face restoration (BFR). Compared with ELIR, PCFlow consistently restores sharper facial structures, including hair, beard, and facial contours, while maintaining more natural textures and local contrast. These improvements lead to visually more faithful reconstructions without introducing noticeable artifacts. Compared with diffusion-based methods, PCFlow produces visually balanced reconstruc- tions without the tendency toward over-sharpened textures observed in DiffBIR, while achieving visual quality competitive with DifFace and PMRF. Notably, these results are obtained using only five inference steps, demonstrating that the 12S. Jo et al. Super Resolution ELIRPMRF(K=3)PMRF(K=25)OursHQInput (LQ) Denoising Inpainting Colorization Fig. 4: Qualitative comparison across image restoration tasks. From left to right: Input (LQ), ELIR, PMRF(K = 3), PMRF(K = 25), PCFlow (Ours), and ground truth image (HQ). PCFlow produces visually sharp and coherent reconstructions even with a small number of integration steps K = 3, establishing an effective training framework that provides a favorable distortion-perception trade-off. proposed framework effectively achieves high perceptual restoration quality with highly efficient inference. Other Restoration Tasks. Fig. 4 presents qualitative comparisons across four image restoration tasks. Compared to ELIR, PCFlow consistently generates vi- sually more coherent and realistic reconstructions. In particular, ELIR tends to generate slightly over-smoothed facial structures, while PCFlow restores sharper facial boundaries and more consistent skin textures, leading to perceptually more faithful reconstructions. Note that PCFlow can occasionally generate subtle ar- tifacts around high-frequency regions such as the eyes. Compared to PMRF with a larger number of integration steps K = 25, PCFlow attains strong perceptual quality while operating in a significantly more efficient few-step regime. These ob- servations align with the quantitative trends in Tab. 2, where PCFlow improves perceptual metrics over ELIR and achieves a favorable distortion-perception trade-off, despite requiring substantially fewer transport steps and model pa- rameters than PMRF(K = 25). 4.4 Ablation Studies We conduct several ablation studies and analyze the contribution of each com- ponent in our proposed PCFlow training objective. Perceptually Consistent Flow Matching for Efficient Image Restoration13 Table 3: Validation of the Preheating Period. The combination of preheating period, gradient surgery, and linear warmup schedule demonstrates the best overall performance in both distortion and perceptual metrics on super-resolution task. SettingL LCPL Preheating λ-scheduling FID↓ PSNR↑ SSIM↑ LPIPS↓ L LCFM only–46.10 23.35 0.6476 0.3373 w/o Gradient Alignment epoch 0×linear warmup 46.40 23.32 0.6484 0.3363 w/ Gradient Alignment epoch 0×linear warmup 46.26 23.31 0.6480 0.3364 PCFlowepoch 250✓linear warmup 45.50 23.38 0.6512 0.3328 Table 4: Ablation on PCFlow components. Quantitative results for adding each PCFlow component on colorization task. The best performance under conditional flow formulation (B–E) is highlighted in bold, while the second-best are underlined . FID↓ PSNR↑ SSIM↑ LPIPS↓ Base (A)56.27 23.11 0.7651 0.3675 + Conditional (B)47.21 21.88 0.7220 0.3845 + Encoder Fine-Tuning (C)45.97 22.190.7465 0.3654 + Perceptual Objective (L LCPL ) (D)45.7822.27 0.7530 0.3551 + Conflict-Free Gradient Alignment (E) 45.21 22.18 0.74990.3596 Preheating Period. Tab. 3 evaluates the contributions of the proposed pre- heating period. The preheating period corresponds to the first 250 epochs, during which only the reconstruction objective is optimized while perceptual supervision is disabled. Jointly training both distortion and perception objectives from the beginning yields inferior results compared to PCFlow, suggesting that the initial preheating stage is essential for establishing a stable coarse-to-fine transport tra- jectory before introducing perceptual supervision. In addition, applying conflict- free gradient alignment from epoch 0 consistently improves FID over naive joint optimization (46.40 → 46.26), indicating that mitigating optimization conflicts between reconstruction and perceptual objectives is beneficial. Combining both components yields the best performance across all metrics. Individual Training Components. Tab. 4 shows quantitative results for pro- gressively adding each of the PCFlow components. For the baseline unconditional model (config A), we set σ min to 0.05 for super-resolution, 0.01 for denoising and colorization, and 0.025 for inpainting task. Training with conditional flow match- ing formulation (config B) improves FID by a substantial margin from 56.27 to 47.21. Fine-tuning the encoder along with the vector field (config C) further enhances model performance in both distortion and perceptual metrics. Adding the perceptual objective (config D) improves perceptual quality while maintain- ing reconstruction fidelity, effectively steering the model towards perceptually sharp data manifolds. Finally, incorporating the proposed conflict-free gradient alignment (config E) achieves the lowest FID of 45.21, pushing the model closer to the optimal distortion–perception tradeoff. We observe that similar trends consistently hold across the remaining image restoration tasks. 14S. Jo et al. Table 5: Ablation on λ-scheduling. Comparison of different scheduling methods for λ LCPL . Increasing the perceptual weight via linear warmup schedule consistently achieves the best model performance in FID across four image restoration tasks. Taskλ-scheduling FID↓ LPIPS↓ Super-Resolution constant46.18 0.3300 linear45.74 0.3326 linear warmup 45.50 0.3328 Denoising constant46.12 0.2790 linear45.48 0.2814 linear warmup 45.42 0.2800 Inpainting constant46.25 0.2918 linear45.56 0.2944 linear warmup 45.50 0.2936 Colorization constant45.78 0.3551 linear45.450.3611 linear warmup 45.21 0.3596 λ-scheduling. We further investigate the role of the perceptual weight λ LCPL as a function of the diffusion timestep t. Tab. 5 shows quantitative comparison of different scheduling methods, including constant, linear, and linear warmup schedules. We observe that linear warmup schedule consistently achieves the best FID across all four image restoration tasks, demonstrating the benefit of grad- ually introducing perceptual supervision during transport. We hypothesize that early transport steps primarily require stable global alignment between degraded observations and the target distribution, where excessive perceptual supervision may introduce unnecessary optimization conflicts. In contrast, as the transport progresses closer to the true image manifold, perceptual supervision becomes more beneficial for recovering fine structures and visually realistic details. 4.5 Analysis on Gradient Conflict We analyze the interaction between reconstruction objectiveL LCFM and percep- tual objective L LCPL by comparing the results from standard joint optimization with our proposed gradient alignment method. As illustrated in Fig. 5, the co- sine similarity heatmap reveals substantial regions of negative alignment (blue) under the standard update, indicating that the two objectives frequently pro- duce conflicting gradients. Such conflicts can hinder stable optimization and slow down convergence. In contrast, after applying the proposed conflict-free update, the gradients exhibit significantly improved alignment, with fewer negatively correlated regions and more consistent positive interactions. Perceptually Consistent Flow Matching for Efficient Image Restoration15 Fig. 5: Analysis of gradient interaction between flow matching and percep- tual objectives. Cosine similarity maps between the LCFM and LCPL gradients as a function of training epochs and log-SNR, shown without (top) and with (bottom) the proposed conflict-free update. Our proposed method significantly mitigates gra- dient conflict, particularly in low-SNR regions, and promotes consistent optimization throughout the sampling process. 5 Conclusion In this paper, we propose PCFlow, a unified latent transport framework for image restoration that jointly optimizes distortion and perceptual quality. By formu- lating the problem with latent consistency flow matching objective, our method directly learns the transport between degraded and clean images, hence enabling efficient few-step inference. To enhance perceptual realism, we additionally intro- duce a latent consistency perceptual objective that enforces semantic alignment along the transport trajectory. Furthermore, motivated by our analysis of the interaction between flow consistency and perceptual objectives, we propose a conflict-free gradient update method that enables the perceptual objective to steer optimization while removing conflicting structural gradient components. 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IEEE/CVF conference on computer vision and pattern recognition. p. 1219–1229 (2023) Supplementary Material for Flow Straight to Reality: Perceptually Consistent Flow Matching for Efficient Image Restoration Sangwoo Jo 1 , Donggeun Ko 2 , Jayeon Kang 1 , Youngsang Kwak 2 , Jaehwa Kwak 2 , and Sungjoon Choi 1 1 Korea University, Seoul, South Korea jasonjo97, nature0213, sungjoonc@korea.ac.kr 2 Aim Future, Seoul, South Korea sean.ko, youngsang.kwak, jaehwa.kwak@aimfuture.ai A Additional Implementation Details A.1 Hyperparameters We provide training hyperparameters for our proposed PCFlow in Tab. 1. Note that although PCFlow can be trained within a single unified procedure, we sep- arate the stages in practice to allow additional flexibility for hyperparameter tuning. For the convolution-only U-Net backbone, we set the number of chan- nels for the downsampling blocks as [128, 256, 256, 512] and number of mid blocks to 3 for blind face restoration (BFR) and 1 for the remaining tasks, following ELIR [6]. For the LCPL objective, we use decoder features as a source of percep- tual supervision, similar to the LPL loss formulation [3]. We set the perceptual objective coefficient λ LCPL to increase over timestep t, i.e., λ LCPL (t) = λ min + I t≥t min (λ max − λ min ) t− t min 1− t min , (1) which progressively shifts the trajectory towards the target manifold. We set λ min = 0, λ max = 0.5, and t min = 0.5 for linear warmup schedule. A.2 Training Details for E-LatentLPIPS In this section, we provide training details for implementing E-LatentLPIPS [12] which serves as an external perceptual supervision in our ablation study. We first train a VGG network [22] on ImageNet dataset [8] with resolution of 256×256 to learn general feature representations in the latent space. We evaluate two variants of the VGG16 backbone with group normalization and batch normalization. We empirically observe that the batch normalization yields higher accuracy, and hence select it as our backbone for the external perceptual network. We subsequently fine-tune the network on BAPPS dataset [30] to align the features with human perceptual similarity judgments. Overall, as illustrated in Tab. 2, our implementation achieves similar performance to the original work [12], despite being trained at resolution of 256×256 and latent space of the Tiny AutoEncoder [20], which is a compressed version of Stable Diffusion VAE [9]. 20S. Jo et al. Table 1: Training hyperparameters for the two training stages of PCFlow. The first column corresponds to blind face restoration tasks (BFR), while the second column corresponds to the remaining four restoration tasks, including super-resolution, de- noising, inpainting, and colorization. (a) PCFlow with LCFM objective only. Hyperparameters Blind Face Restoration Other Restoration tasks Parameters32M21M Euler steps (M)53 CFM segments (K)53 CFM ∆t0.050.05 CFM α0.0010.001 σ min 10 −5 10 −5 Training epochs250250 Batch size32128 Image dimension3× 512× 5123× 256× 256 Latent dimension16× 64× 6416× 32× 32 Precisionbfloat16 mixedbfloat16 mixed Training hardware1× H100 80GB1× A100 80GB Training time2 days1 day OptimizerAdamWAdamW Learning rate2× 10 −4 2× 10 −4 AdamW betas(0.9, 0.999)(0.9, 0.999) Weight decay0.020.02 EMA decay0.9990.999 (b) PCFlow with perceptual objective (LCPL). Hyperparameters Blind Face Restoration Other Restoration tasks Parameters32M21M Euler steps (M)53 CFM segments (K)53 CFM ∆t0.050.05 CFM α0.0010.001 σ min 10 −5 10 −5 Training epochs250250 Batch size32128 Image dimension3× 512× 5123× 256× 256 Latent dimension16× 64× 6416× 32× 32 Precisionbfloat16 mixedbfloat16 mixed Training hardware1× H100 80GB1× A100 80GB Training time2.5 days2 days OptimizerAdamWAdamW Learning rate2× 10 −4 2× 10 −4 AdamW betas(0.9, 0.999)(0.9, 0.999) Weight decay0.020.02 EMA decay0.9990.999 w l [1, 0.5, 0.25, 0.125, 1][1, 0.5, 0.25, 0.125, 1] λ LCPL (t)linear warmuplinear warmup λ min 00 λ max 0.50.5 t min 0.50.5 Perceptually Consistent Flow Matching for Efficient Image Restoration21 Table 2: ImageNet and BAPPS Classification Scores. Classification accuracy on ImageNet and BAPPS datasets within the Tiny AutoEncoder latent space. Our reimplementation achieves similar performance to the original E-LatentLPIPS paper. DatasetTypeOursE-LatentLPIPS (Original) ImageNetVGG-BN67.8268.26 Traditional76.6274.29 BAPPSCNN82.4381.99 Real63.7963.21 B Additional Results B.1 Further Ablation Studies Unconditional vs. Conditional Flow Models. We consider both uncondi- tional and conditional flow formulations. We empirically find that the conditional flow model consistently achieves better FID across all restoration tasks, as shown in Tab. 3. Unlike PMRF, which reports limited gains from conditional transport, we observe that initializing from random noise allows the model to fully leverage its generative capability. From an optimal transport perspective, the uncondi- tional formulation may restrict the transport trajectory to remain close to the degraded manifold, whereas the conditional formulation enables transport with generative prior resulting in higher perceptual realism. Table 3: Ablation on Unconditional vs. Conditional Flow Models. Learning a transport from random noise with degraded image as a conditional input leads to substantial improvements in FID over unconditional formulation. TaskConditional FID↓ LPIPS↓ Super-Resolution ✗63.69 0.3509 ✓46.42 0.3396 Denoising ✗48.50 0.2866 ✓45.70 0.3025 Inpainting ✗60.47 0.3677 ✓47.04 0.3611 Colorization ✗56.27 0.3675 ✓47.21 0.3845 Encoder Fine-Tuning. We compare freezing the pretrained encoder against jointly fine-tuning it together with the vector field network. As shown in Tab. 4, 22S. Jo et al. Table 4: Ablation on Encoder Fine-Tuning (FT). Comparison of PCFlow and with and without encoder fine-tuning. Fine-tuning encoder along with the vector field shows better performance in both distortion and perception metrics across all four image restoration tasks. TaskEncoder FT FID↓ PSNR↑ SSIM↑ LPIPS↓ Super-Resolution w/o46.42 23.30 0.6462 0.3396 w/46.10 23.35 0.6476 0.3373 Denoising w/o45.70 25.50 0.7215 0.3025 w/45.29 26.18 0.7437 0.2857 Inpainting w/o47.04 22.33 0.6318 0.3611 w/45.64 24.82 0.7150 0.2990 Colorization w/o47.21 21.88 0.7220 0.3845 w/45.97 22.19 0.7465 0.3654 fine-tuning the encoder consistently improves both reconstruction and perceptual quality across all image restoration tasks. For instance, for super-resolution, FID and LPIPS decrease from 46.42 to 46.10 and from 0.3396 to 0.3373, respectively, while PSNR and SSIM increase from 23.30 to 23.35 and from 0.6462 to 0.6476, respectively. Similar improvements are observed in other image restoration tasks. We hypothesize that, since the encoder is pretrained on high-quality images, it requires additional training to fully learn the representation of degraded inputs. Joint optimization therefore allows the encoder to adapt to the degradation distribution, resulting in improved alignment between the latent representation and the restoration dynamics. Perceptual Network. We compare the effect of using external and internal perceptual networks for perceptual supervision, as summarized in Tab. 5. Note that external network corresponds to our reimplementation of E-LatentLPIPS, and the internal network corresponds to using intermediate and final decoder fea- tures. Using the external perceptual network improves distortion metrics such as PSNR and SSIM. However, applying the proposed gradient alignment with the following external network does not lead to further improvements and in- stead yields the model to deviate from the optimal trajectory. This suggests that perceptual supervision derived from the VGG network trained on an external dataset may not be suitable for restoration dynamics. In contrast, defining the perceptual objective based on internal decoder fea- tures leads to improved perceptual alignment with the restoration objective. In particular, incorporating the proposed conflict-free gradient alignment further reduces FID from 46.01 to 45.50, yielding the best perceptual quality among all configurations. The following results suggest that internal perceptual represen- tations are better aligned with the latent restoration dynamics, and that the proposed gradient alignment strategy further stabilizes the interaction between Perceptually Consistent Flow Matching for Efficient Image Restoration23 Table 5: Ablation on Perceptual Network. Comparison between external percep- tual supervision (E-LatentLPIPS) and internal decoder feature supervision for super- resolution task. Conflict-free gradient alignment further improves perceptual quality when applied to the internal perceptual network, achieving the best FID. Perceptual NetworkFID↓ PSNR↑ SSIM↑ LPIPS↓ External46.03 23.58 0.6604 0.3223 + Conflict-Free Gradient Alignment 46.15 23.41 0.6514 0.3299 Internal46.01 23.31 0.6515 0.3310 + Conflict-Free Gradient Alignment 45.50 23.38 0.6512 0.3328 reconstruction and perceptual objectives. Hence, we adopt the internal percep- tual network with conflict-free gradient alignment as our final configuration. Perceptual vs. Structural Gradient Projection. We further compare two conflict-resolution strategies: projecting the perceptual gradient (g LCPL → ̃g LCPL ) and projecting the structural gradient (g LCFM → ̃g LCFM ). As shown in Tab. 6, projecting the structural gradient generally yields better FID across all restora- tion tasks. These results support our design choice of treating the perceptual objective as a steering signal and resolving optimization conflicts through struc- tural gradient projection. We hypothesize that perceptual supervision primarily guides the transport trajectory toward perceptually realistic regions of the tar- get manifold, whereas the structural objective provides reconstruction-oriented updates. In addition, we observe that the perceptual gradient exhibits a larger magnitude than the structural gradient, which may further contribute to the improved optimization stability of structural-gradient projection. Table 6: Ablation on Gradient Projection. Quantitative comparison between pro- jecting the perceptual gradient and projecting the structural gradient during conflict- free gradient alignment. Projecting the structural gradient g LCFM → ̃g LCFM generally yields better model performance in FID across restoration tasks. TaskGradient Projection FID↓ LPIPS↓ Super-Resolution g LCPL → ̃g LCPL 45.66 0.3317 g LCFM → ̃g LCFM 45.50 0.3328 Denoising g LCPL → ̃g LCPL 45.42 0.2800 g LCFM → ̃g LCFM 45.42 0.2800 Inpainting g LCPL → ̃g LCPL 45.53 0.2935 g LCFM → ̃g LCFM 45.50 0.2936 Colorization g LCPL → ̃g LCPL 45.21 0.3599 g LCFM → ̃g LCFM 45.21 0.3596 24S. Jo et al. B.2 Further Analysis Fig. 1 compares the transport trajectories of PCFlow compared with its base- lines, ELIR [6] and PMRF [19]. PMRF exhibits unstable structural progression across timesteps. Early predictions remain overly smooth and high-frequency details appear abruptly, resulting in inconsistent intermediate states. ELIR at- tempts to introduce perceptual details from the beginning of the trajectory. How- ever, these details are structurally inconsistent, suggesting that the model pri- oritizes texture synthesis before sufficiently recovering the underlying structure. In contrast, PCFlow follows a coarse-to-fine restoration trajectory. PCFlow pri- marily recovers the global facial structure in early steps, whereas high-frequency details such as hair texture and eye boundaries are progressively refined in later timesteps. t= 1/3t = 2/3t= 1t = 1/3t = 2/3t = 1 PMRF ELIR Ours Fig. 1: Comparison in trajectory of PCFlow with its baselines. PCFlow ex- hibits a stable coarse-to-fine refinement trajectory, where global structure is initially re- covered in early steps and fine details are progressively introduced. In contrast, PMRF produces inconsistent intermediate states, while ELIR introduces perceptual details prematurely, often leading to structurally inconsistent textures. B.3 Further Qualitative Results Perceptually Consistent Flow Matching for Efficient Image Restoration25 Input (LQ) ELIRPMRF(K=3) PMRF(K=25) OursHQ Fig. 2: Additional Results of PCFlow on super-resolution task. From left to right: Input(LQ), ELIR, PMRF(K = 3), PMRF(K = 25), PCFlow(Ours), and ground truth image(HQ). Input (LQ) ELIRPMRF(K=3) PMRF(K=25) OursHQ Fig. 3: Additional Results of PCFlow on denoising task. From left to right: Input(LQ), ELIR, PMRF(K = 3), PMRF(K = 25), PCFlow(Ours), and ground truth image(HQ). 26S. Jo et al. Input (LQ) ELIRPMRF(K=3) PMRF(K=25) OursHQ Fig. 4: Additional Results of PCFlow on inpainting task. From left to right: Input(LQ), ELIR, PMRF(K = 3), PMRF(K = 25), PCFlow(Ours), and ground truth image(HQ). Input (LQ) ELIRPMRF(K=3) PMRF(K=25) OursHQ Fig. 5: Additional Results of PCFlow on colorization task. From left to right: Input(LQ), ELIR, PMRF(K = 3), PMRF(K = 25), PCFlow(Ours), and ground truth image(HQ).