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ScaleResfusion: Residual Rectified Flow based on Residual Vector Field
Zhenning Shi, Chen Xu, Junhao Zhang, Kefei Zhang, Linjie Liu, Zhedong Zheng, Tao Li
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
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Summary
The paper introduces ScaleResfusion, a scalable diffusion framework for real-world image restoration that adapts pre-trained text-to-image rectified-flow models. It proposes Residual Rectified Flow (RRF), which incorporates a residual term into the standard rectified flow trajectory, allowing the diffusion process to start from noisy low-quality images rather than pure Gaussian noise. This approach enables parameter-efficient fine-tuning using Low-Rank Adaptation (LoRA) and includes a knowledge-distillation pipeline to reduce sampling costs while maintaining high restoration quality.
Entities (6)
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ScaleResfusion → appliedto → Real-World Image Restoration
confidence 96% · ScaleResfusion, a scalable diffusion framework for real-world image restoration
ScaleResfusion → uses → Residual Rectified Flow
confidence 95% · The core of our method is Residual Rectified Flow, which introduces the residual term R into Standard Rectified Flow.
ScaleResfusion → uses → Rectified Flow
confidence 92% · built on pre-trained text-to-image rectified-flow models
Residual Rectified Flow → enables → Low-Rank Adaptation
confidence 90% · ScaleResfusion can efficiently adapt large pre-trained backbones with only Low-Rank Adaptation (LoRA)
ScaleResfusion → uses → Knowledge Distillation
confidence 88% · We further introduce a knowledge-distillation pipeline to reduce sampling cost
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Abstract
Abstract:Real-world Image Restoration (Real-IR) aims to recover high-quality (HQ) images from complex and unknown degradations. Although recent diffusion-based methods have substantially improved perceptual quality, their current designs leave two key challenges unresolved. Methods that start from Gaussian noise are slow and often less faithful to the degraded input. Residual-based methods usually train from scratch, which makes it hard to exploit modern pre-trained generative priors. In this paper, we present ScaleResfusion, a scalable diffusion framework for real-world image restoration built on pre-trained text-to-image rectified-flow models. The core of our method is Residual Rectified Flow, which introduces the residual term R into Standard Rectified Flow. Instead of starting from pure noise, it uses a residual transport path that starts from noisy low-quality (LQ) images and admits an exact acceleration point. By learning the residual vector field, Residual Rectified Flow keeps the output distribution and linear diffusion process consistent with the pre-trained rectified-flow models. This makes parameter-efficient fine-tuning possible at scale. We further introduce a knowledge-distillation pipeline to reduce sampling cost while maintaining restoration quality. Extensive experiments on multiple real-world restoration tasks show that ScaleResfusion achieves state-of-the-art performance with much higher efficiency. These results suggest a practical and scalable way to adapt large pre-trained diffusion models to real-world image restoration. Our code and models are available at this https URL.
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- Source: https://arxiv.org/abs/2607.25275v1
- Canonical: https://arxiv.org/abs/2607.25275v1
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ScaleResfusion: Residual Rectified Flow based on Residual Vector Field Zhenning Shi1,* Chen Xu2,* Junhao Zhang3 Kefei Zhang1 Linjie Liu4 Zhedong Zheng2,† Tao Li1,† 1Nankai University, Tianjin, China 2University of Macau, Macau, China 3Csiro Data 61, Australia 4Beihang University, Beijing, China *Equal Contribution. † Authors: litao@nankai.edu.cn, zhedongzheng@um.edu.mo. Abstract. Real-world Image Restoration (Real-IR) aims to recover high-quality (HQ) images from complex and unknown degradations. Although recent diffusion-based methods have substantially improved perceptual quality, their current designs leave two key challenges unresolved. Methods that start from Gaussian noise are slow and often less faithful to the degraded input. Residual-based methods usually train from scratch, which makes it hard to exploit modern pre-trained generative priors. In this paper, we present ScaleResfusion, a scalable diffusion framework for real-world image restoration built on pre-trained text-to-image rectified-flow models. The core of our method is Residual Rectified Flow, which introduces the residual term R into the Standard Rectified Flow. Instead of starting from pure noise, it uses a residual transport path that starts from noisy low-quality (LQ) images and admits an exact acceleration point. By learning the residual vector field, Residual Rectified Flow keeps the output distribution and linear diffusion process consistent with the pre-trained rectified-flow models. This makes parameter-efficient fine-tuning possible at scale. We further introduce a knowledge-distillation pipeline to reduce sampling cost while maintaining restoration quality. Extensive experiments on multiple real-world restoration tasks show that ScaleResfusion achieves state-of-the-art performance with much higher efficiency. These results suggest a practical and scalable way to adapt large pre-trained diffusion models to real-world image restoration. Our code and model are available at github.com/YukinoshitaLove/ScaleResfusion. Diffusion-based Models, Residual Diffusion Models, Real World Image Restoration, Image Super-Resolution. Figure 1. Visual examples of ScaleResfusion for Real-IR. The top row shows LQ inputs and the bottom row shows our restored results with only 4 sampling steps. ScaleResfusion preserves the structure, identity, and content of the input images while synthesizing photo-realistic details. 1. Introduction Image restoration (IR) aims to recover a high-quality (HQ) image from low-quality (LQ) observations (Dong et al., 2014; Dai et al., 2019; Zhang et al., 2018b, 2017; Chen et al., 2021; Liang et al., 2021; Zhang et al., 2022a; Chen et al., 2023; Ledig et al., 2017; Wang et al., 2018, 2021b). In real-world image restoration (Real-IR), the degradation process is usually complex, unknown, and compound, making the inverse problem highly ill-posed in practical scenarios (Zhang et al., 2021; Wang et al., 2021b). The central challenge is to recover realistic details while preserving fidelity to the degraded input. Recently, diffusion-based models (Ho et al., 2020; Song et al., 2020a; Song and Ermon, 2019; Song et al., 2020b; Lipman et al., 2022; Liu et al., 2022) have shown remarkable ability in synthesizing high-fidelity restored images (Saharia et al., 2022; Özdenizci and Legenstein, 2023; Whang et al., 2022; Wang et al., 2025b; Guo et al., 2023; He et al., 2025). To leverage the powerful prior knowledge of pre-trained text-to-image (T2I) diffusion models (Rombach et al., 2022; Esser et al., 2024), recent works (Lin et al., 2024; Wang et al., 2024; Yang et al., 2024; Wu et al., 2024b; Yu et al., 2024) introduce the LQ image as a conditional input (Zhang et al., 2023), producing more realistic images than GAN-based methods with more stable training. However, these methods usually consider only LQ images as the condition and start diffusion from Gaussian noise, resulting in lengthy inference and weak consistency between the generated output and the LQ input. Although some works (Wu et al., 2024a; Dong et al., 2025; Li et al., 2025) reduce diffusion steps through knowledge distillation to achieve single-step inference, they tend to learn a LQ-HQ mapping while abandoning the multi-step sampling characteristic of diffusion models, leading to reduced diversity and fidelity. Another line of diffusion-based restoration methods (Delbracio and Milanfar, 2023; Kawar et al., 2022; Luo et al., 2023a, b; Liu et al., 2023; Yue et al., 2023; Shi et al., 2024; Wang et al., 2025a) starts the diffusion process from noisy LQ images rather than Gaussian noise, reducing inference steps while preserving the sampling capability of diffusion models. However, these works typically train a new diffusion model from scratch. Their training objectives and customized noise schedulers often deviate from the output distribution and diffusion process of modern pre-trained models, making direct reuse difficult. Resfusion (Shi et al., 2024) addresses this issue in DDPM (Ho et al., 2020) by learning the resnoise and unifying training and inference through a smooth equivalence transformation. Nevertheless, modern pre-trained models (Esser et al., 2024; Cai et al., 2025; Labs, 2025) are typically based on Rectified Flow (Liu et al., 2022), preventing vanilla Resfusion from scaling further. To solve the problems mentioned above, we propose ScaleResfusion, a scalable diffusion framework that adapts pre-trained T2I Rectified Flow models to Real-IR tasks. Its core is Residual Rectified Flow, which incorporates the image residual into the Rectified Flow trajectory while preserving its linear transport form. This design allows sampling to start from a noisy LQ image instead of pure Gaussian noise, reducing redundant generation steps without discarding the stochastic sampling behavior of diffusion models. Since the optimization target residual vector field only differs from the standard Rectified Flow target by a residual offset, ScaleResfusion can efficiently adapt large pre-trained backbones with only Low-Rank Adaptation (LoRA) (Hu et al., 2022). We further introduce a knowledge-distillation based parameter-efficient fine-tuning (PEFT) pipeline to reduce training and inference cost. Experiments show that ScaleResfusion achieves state-of-the-art performance on multiple Real-IR tasks with significantly faster inference. Our contributions can be summarized as follows: (1) We formulate Residual Rectified Flow for Real-IR by incorporating image residuals into the Rectified Flow trajectory, enabling the diffusion process to start directly from noisy LQ images within the Rectified Flow framework. (2) We derive the residual vector field as the optimization target, which differs from the standard Rectified Flow target only by a residual offset and thus enables LoRA-only PEFT for pre-trained models based on Rectified Flow. (3) Based on ScaleResfusion, we construct an efficient training pipeline with knowledge distillation, demonstrating that residual-based diffusion models can be scaled to billion-scale pre-trained models for Real-IR with only 4 sampling steps. 2. Related Work Traditional Real-IR methods typically learn a direct LQ-to-HQ mapping under simplified or synthetic degradations (Dong et al., 2014; Zhang et al., 2017, 2018b; Chen et al., 2021; Liang et al., 2021; Zhang et al., 2022a; Chen et al., 2023; Wang et al., 2021b), while GAN-based methods improve perceptual realism by matching the natural image distribution (Goodfellow et al., 2014; Ledig et al., 2017; Wang et al., 2018; Zhang et al., 2021; Liang et al., 2022). However, these methods often suffer from over-smoothed details, unstable adversarial training, or uncontrollable artifacts. These limitations have shifted recent Real-IR research toward diffusion-based restoration, which offers stronger generative priors and a more stable training paradigm. In this context, we summarize current diffusion-based methods from two perspectives: diffusion models initialized from Gaussian noise and those initialized from noisy LQ images. Diffusion models initialized from Gaussian noise. Recent Real-IR methods often leverage pre-trained T2I diffusion priors by injecting the LQ image as a condition while keeping the original Gaussian noise initialization. StableSR (Wang et al., 2024) balances fidelity and perceptual quality by fine-tuning a time-aware encoder and using controllable feature wrapping. DiffBIR (Lin et al., 2024) restores the LR images with a reconstruction network and then uses Stable Diffusion (Rombach et al., 2022) to synthesize realistic details. SeeSR (Wu et al., 2024b) extracts semantic features from the input image to better activate the generative prior of Stable Diffusion. PASD (Yang et al., 2024) combines pixel-aware cross-attention with degradation-robust guidance to preserve local structure during generation. SUPIR (Yu et al., 2024) further improves generative fidelity through negative-quality prompts, restoration-guided sampling, and larger-scale pre-training. Overall, despite promising perceptual quality, these methods still sample from Gaussian white noise with the LQ image only as a condition, leading to 20–50 step inference and weak input consistency. This motivates our Residual Rectified Flow’s noisy-LQ initialization. Figure 2. Initialization comparison from a transport perspective. (a) Gaussian-noise initialization starts far from the restoration manifold and induces unstable paths. (b) One-step restoration starts from the LQ observation but collapses the generative restoration process into a deterministic LQ-to-HQ mapping, losing the sampling capability of diffusion models. (c) Noisy-LQ-initialized DDPM sampling injects stochasticity, yet it biases the reverse path toward the input degradation without an explicit residual correction direction. (d) ScaleResfusion starts from a noisy LQ state and follows a residual-oriented transport, producing a closer initialization and more coherent convergence toward the target distribution. Diffusion models initialized from noisy LQ images. To reduce inference cost, OSEDiff (Wu et al., 2024a), TSD-SR (Dong et al., 2025), and FluxSR (Li et al., 2025) distill pre-trained diffusion priors into a direct LQ-to-HQ mapping for one-step restoration. While efficient, they largely replace iterative sampling with a deterministic mapping, which may reduce diversity and fidelity. Other works preserve iterative sampling by initializing diffusion from noisy LQ images. IR-SDE (Luo et al., 2023a) models degradation and restoration with a mean-reverting stochastic differential equation. Refusion (Luo et al., 2023b) performs realistic large-size restoration through latent-space diffusion. ResShift (Yue et al., 2023) accelerates super-resolution by shifting the residual between LQ and HQ images. Residual Denoising Diffusion Models (RDDM) (Liu et al., 2024a) jointly model the residual and noise terms. Resfusion (Shi et al., 2024) learns resnoise to unify training and inference through a smooth equivalence transformation, preserving consistency with the original diffusion process. Overall, noisy-LQ initialization shortens the sampling trajectory while preserving the diffusion sampling nature, but most existing methods train task-specific diffusion models from scratch and use customized objectives or schedulers, making them difficult to reuse with pre-trained T2I priors. This motivates our ScaleResfusion, which starts from noisy LQ images while remaining consistent with the pre-trained Rectified Flow process. 3. Method 3.1. Preliminaries Denoising Diffusion Probabilistic Models (DDPM) (Ho et al., 2020) aim to approximate the real data distribution p(x0)p(x_0) with the learned model distribution pθ(x0)p_θ(x_0) through a discrete Markov chain. Flow-based generative models (Lipman et al., 2022; Liu et al., 2022) improve sampling efficiency by replacing the discrete Markovian process with a continuous transport path between a data sample x0∼p(x0)x_0 p(x_0) and Gaussian noise ϵ∼(0,I)ε (0,I), formulated as (1) xt=atx0+btϵ,t∈[0,1].x_t=a_tx_0+b_tε,t∈[0,1]. The goal is to learn a vector field vθ(xt,t)v_θ(x_t,t) that approximates the target vector field along this path. Rectified Flow (RF) (Liu et al., 2022) adopts the linear path xt=(1−t)x0+tϵx_t=(1-t)x_0+tε and optimizes (2) ℒRF=∫01x0,ϵ[‖vθ(xt,t)−(ϵ−x0)‖2]t.L_RF= _0^1E_x_0,ε [ \|v_θ(x_t,t)-(ε-x_0) \|^2 ]dt. Sampling is performed by solving the reverse ODE (3) x0=x1+∫10vθ(xτ,τ)τ,x_0=x_1+ _1^0v_θ(x_τ,τ)dτ, This Gaussian-to-image transport is effective for generic generation, but it is redundant for image restoration since the LQ image itself already carries effective information. 3.2. Residual Modeling for Image Restoration Given an LQ–HQ image pair, we denote the LQ observation and the HQ target as x^0 x_0 and x0x_0 respectively, and define the residual term as (4) R=x^0−x0.R= x_0-x_0. Conditioned on the observed LQ image x^0 x_0, recovering x0x_0 is therefore equivalent to estimating the correction R, since x0=x^0−Rx_0= x_0-R. This residual formulation is particularly suitable for restoration: the LQ image already preserves most semantic layout and coarse structures, while the residual mainly captures local degradation artifacts, high-frequency details, and texture corrections. Figure 3. The residual term R exhibits consistent low-energy, edged patterns in both the spatial and frequency domains, suggesting that RRF only needs to learn a compact residual update around the pre-trained transport. As shown in Fig. 3, the residual is much more compact than either the LQ or HQ image. In the spatial domain, R appears as a low-amplitude and localized correction around edges, textures, and degradation artifacts. After the Scaled Fourier Transform, it also exhibits substantially lower spectral energy than the image signals. This observation suggests that the task-specific transformation for restoration is concentrated in a compact residual subspace, rather than being distributed across the full image-generation process. Such a localized and energy-limited update is naturally compatible with LoRA (Hu et al., 2022), which is designed to capture low-rank adaptations around a pre-trained model. Figure 4. Geometric Interpretation of Residual Rectified Flow (RRF). (a) RRF introduces the weighted residual term γRγ R into the diffusion path, yielding a straight trajectory that intersects the implicit noise-to-LQ path at the acceleration point. (b) Standard Rectified Flow transports Gaussian noise to the HQ image distribution through a linear ODE. (c) Starting from the noisy-LQ state xt⋆∼(γ1+γx^0,1(1+γ)2Σ)x_t ( γ1+γ x_0, 1(1+γ)^2 ), RRF learns the residual vector field resvresv to recover the HQ image x0x_0 over a shortened sampling interval. The residual formulation is also preferable from a transport perspective. The reverse ODE is initialization-sensitive: under standard stability assumptions, an initial state closer to the task-relevant restoration manifold is more likely to be transported to a terminal state close to the desired HQ distribution. Pure Gaussian initialization is task-agnostic and far from the observed content, whereas residual modeling preserves the structural prior in x^0 x_0 and makes the transport correction-oriented through R. Fig. 2 compares different strategies: Gaussian initialization suffers from large initial discrepancy; one-step restoration (OSEDiff) loses the sampling capability of diffusion models by using a deterministic LQ-to-HQ mapping; and Noisy-LQ-initialized DDPM sampling (ResShift) remains degradation-biased without an explicit residual direction. In contrast, ScaleResfusion starts from a noisy LQ state and follows a residual-oriented path, yielding more coherent trajectories and lower endpoint error. A formal measure-transport analysis is provided in Appendix A. Overall, the above analysis shows that residual modeling provides both a compact learning target and a better-aligned transport perspective. This motivates a residual-oriented flow that starts from a noise LQ state and transports along an explicit correction direction. The next subsection formalizes this idea as a continuous Residual Rectified Flow trajectory. 3.3. Residual Rectified Flow Following the residual definition in Eq. (4), the proposed Residual Rectified Flow (RRF) introduces the weighted residual term into the RF trajectory in Eq. (1). Given a residual ratio γ>0γ>0, t∈[0,1]t∈[0,1], and ϵ∼(0,I)ε (0,I), RRF constructs (5) xt=(1−t)x0+tγR+tϵ.x_t=(1-t)x_0+tγ R+tε. The trajectory is a straight line connecting the HQ image x0x_0 and the endpoint γR+ϵγ R+ε, whose target velocity is constant with respect to t: (6) ut(xt∣x0,ϵ,R)=dxtdt=resv=γR+ϵ−x0.u_t(x_t x_0,ε,R)= dx_tdt=resv=γ R+ε-x_0. As shown in Fig. 4, the blue arrow represents the linear diffusion process of Standard Rectified Flow (RF), which is an ODE from the Gaussian distribution to the HQ image distribution. While the purple arrow represents the proposed Residual Rectified Flow (RRF), which constructs a continuous path between x0x_0 and a noisy weighted residual term γR+ϵγ R+ε. In the diffusion process of RRF, it implicitly reduces the residual term R between x0x_0 and x0 x_0 with the residual vector field. By the definition of similar triangles, we can obtain the expression for xtx_t as in Eq. (5), where the coefficient of γRγ R is t. When we define xt^=(1−t)x0^+tϵ x_t=(1-t) x_0+tε with the same Gaussian noise ϵε as in xtx_t, the gray arrow represents an implicit Rectified Flow diffusion process from the Gaussian distribution to the LQ image x0 x_0 distribution. Due to the residual term R, the trajectories of RRF and the implicit Rectified Flow are constrained on the same hyperplane, and their intersection is the acceleration point (Shi et al., 2024). The proposed Residual Rectified Flow admits an exact acceleration point due to its continuous ODE trajectory. Substituting R=x^0−x0R= x_0-x_0 into Eq. (5) gives: (7) xt=(1−t)x0+tγ(x^0−x0)+tϵ=(1−(1+γ)t)x0+tγx^0+tϵ.x_t=(1-t)x_0+tγ( x_0-x_0)+tε=(1-(1+γ)t)x_0+tγ x_0+tε. The coefficient of x0x_0 vanishes when 1−(1+γ)t⋆=01-(1+γ)t =0, which leads to the exact acceleration point t⋆=11+γt = 11+γ. At this point, the state of RRF can be completely represented by the LQ image x0 x_0 and noise ϵε, no longer depending on the unknown HQ image x0x_0, thereby enabling accelerated sampling. Accordingly, RRF trains a neural residual velocity field resvθ(xt,t)resv_θ(x_t,t) only over the effective interval [0,t⋆][0,t ]: (8) ℒRRF=∫0t⋆[‖resvθ(xt,t)−(γR+ϵ−x0)‖2]t.L_RRF= _0^t E [ \|resv_θ(x_t,t)-(γ R+ε-x_0) \|^2 ]dt. In the diffusion process of RRF, it actually starts from the acceleration point t⋆t with the initial distribution being (γ1+γx^0,1(1+γ)2Σ)N ( γ1+γ x_0,\ 1(1+γ)^2 ). We can obtain its signal-to-noise ratio (SNR) as (9) SNR(xt⋆)∝γ1+γ11+γ=γ.SNR(x_t ) γ1+γ 11+γ=γ. Thus, the residual ratio γ directly controls the SNR level of the starting point: larger γ yields an initialization closer to the LQ image, while smaller γ injects stronger Gaussian randomness. During sampling, RRF starts from xt⋆x_t and integrates the learned ODE x0=xt⋆+∫t⋆0resvθ(xτ,τ)τx_0=x_t + _t ^0resv_θ(x_τ,τ)dτ to the data endpoint. As formalized in Eq. (5) and Eq. (6), and detailed in Algorithm 1, RRF preserves the Standard Rectified Flow structure and only introduces residual offsets: xt=xtRF+tγRx_t=x_t^RF+tγ R and resv=vRF+γRresv=v^RF+γ R. Therefore, adapting a pre-trained diffusion model to RRF does not require relearning the image-noise transport, but only fitting a compact residual correction. We thus adopt pure LoRA (Hu et al., 2022) as the PEFT strategy, keeping the pre-trained backbone fixed while learning low-rank updates for the residual vector field. The resulting parameter-efficient implementation is described in the following training pipeline. 3.4. Knowledge-Distilled Parameter-Efficient Training Pipeline Based on the residual theory above, we design ScaleResfusion, a parameter-efficient training pipeline that distills pre-trained diffusion priors into an RRF generator. As shown in Fig. LABEL:fig:ScaleResfusion, ScaleResfusion contains a generation branch and a regularization branch. Both branches share the same frozen pre-trained backbone weights, while trainable LoRA adapters learn the residual task update. Given an LQ–HQ pair (x^0,x0)( x_0,x_0), we encode images into the latent space with a frozen VAE and train a LoRA-adapted generator GθG_θ to predict the residual velocity resvθ=Gθ(xt,t)resv_θ=G_θ(x_t,t). The LQ features are injected into the restored-image generator through Ref Attention (Shi et al., 2025; Hu, 2024). We further use DAPE (Wu et al., 2024b) to provide additional textual constraints. For notation simplicity, xtx_t denotes the latent RRF state, and image-space losses are computed after VAE decoding. We convert the residual velocity output into an equivalent prediction to compute losses on the predicted clean restoration, where the VAE decoder is omitted in notation for image-space losses: (10) x0pred=xt−tresvθ(xt,t).x_0^pred=x_t-t\,resv_θ(x_t,t). Data term. The data objective enforces pairwise fidelity and perceptual consistency: (11) ℒdata=λmseℒMSE(x0pred,x0)+λlpipsℒLPIPS(x0pred,x0).L_data= _mseL_MSE(x_0^pred,x_0)+ _lpipsL_LPIPS(x_0^pred,x_0). Here ℒMSEL_MSE penalizes pixel-wise reconstruction errors and preserves the pairwise fidelity to the HQ target, while ℒLPIPSL_LPIPS measures perceptual similarity in a deep feature space (Zhang et al., 2018a) to encourage visually consistent structures and textures. Regularization term. To align the restored distribution with natural HQ images, we introduce a regularization term that combines a DMD loss and an optional GAN loss: (12) ℒreg=λdmdℒDMD(x0pred)+λganℒGAN(x0pred).L_reg= _dmdL_DMD(x_0^pred)+ _ganL_GAN(x_0^pred). The DMD term serves as a knowledge-distillation objective following the real/fake regularizer design (Yin et al., 2024b). Specifically, the frozen pre-trained regularizer acts as the teacher that provides the real diffusion prior, and the RRF generator is the student that learns to produce samples aligned with this prior. The LoRA-adapted fake regularizer is trained with ℒdiffL_diff on generated samples to estimate the generator-induced distribution, providing the fake score needed by DMD. Through this teacher–student distillation, ℒDMDL_DMD transfers the natural-image prior of the pre-trained diffusion model to the RRF generator and encourages restored images to stay on the HQ image manifold. The optional GAN term further sharpens local details by adversarially matching the restored distribution to real HQ images. Table 1. Quantitative comparison across real-world and synthetic benchmarks. Higher values indicate better performance for PSNR, SSIM, MUSIQ, and MANIQA, while lower values indicate better performance for LPIPS, DISTS, FID, and NIQE. Methods include diffusion-based baselines and our FLUX2-4B variant. The best and second-best results of each metric are highlighted in red and blue. We also report NFE and inference time to compare efficiency. See the Appendix for the full comparison and more datasets. Datasets Method NFE Inf. Time (ms) PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ NIQE ↓ MUSIQ ↑ MANIQA ↑ ResShift 15 848 27.05 0.74 0.39 0.26 159.90 8.65 51.24 0.47 StableSR 200 12,036 28.04 0.75 0.33 0.23 144.15 6.60 58.53 0.56 CCSR 6 516 28.24 0.78 0.32 0.23 157.30 6.81 66.28 0.61 SeeSR 50 4,445 28.07 0.77 0.32 0.23 147.37 6.41 65.09 0.61 SUPIR 50 25,252 25.09 0.65 0.42 0.28 169.48 7.39 58.79 0.55 OSEDiff 1 266 27.92 0.78 0.30 0.22 135.41 6.46 64.69 0.59 [gray]0.95 DRealSR Ours (w/o GAN) 4 646 29.77 0.82 0.25 0.20 118.18 6.95 62.42 0.61 [gray]0.95 Ours (w/ GAN) 4 646 28.26 0.78 0.29 0.21 124.03 6.21 65.16 0.64 ResShift 15 848 25.66 0.74 0.33 0.25 128.03 8.07 56.89 0.51 StableSR 200 12,036 24.62 0.70 0.31 0.22 128.54 5.78 65.48 0.62 CCSR 6 516 25.92 0.75 0.28 0.21 122.84 5.73 69.18 0.64 SeeSR 50 4,445 25.15 0.72 0.30 0.22 125.30 5.40 69.81 0.65 SUPIR 50 25,252 23.65 0.66 0.35 0.25 130.38 6.11 62.09 0.58 OSEDiff 1 266 25.15 0.73 0.29 0.21 123.53 5.65 69.08 0.63 [gray]0.95 RealSR Ours (w/o GAN) 4 646 27.05 0.78 0.24 0.20 104.74 6.21 67.25 0.64 [gray]0.95 Ours (w/ GAN) 4 646 25.78 0.75 0.26 0.20 106.22 5.29 69.86 0.68 ResShift 15 848 24.59 0.62 0.31 0.21 30.81 6.92 58.90 0.53 StableSR 200 12,036 23.27 0.57 0.31 0.20 24.95 4.77 65.78 0.62 CCSR 6 516 24.30 0.63 0.30 0.20 30.84 5.34 69.53 0.61 SeeSR 50 4,445 23.68 0.60 0.32 0.20 25.89 4.81 68.66 0.62 SUPIR 50 25,252 22.13 0.53 0.39 0.23 31.40 5.68 63.86 0.59 OSEDiff 1 266 23.72 0.61 0.29 0.20 26.34 4.71 67.96 0.61 [gray]0.95 DIV2K-Val Ours (w/o GAN) 4 646 24.90 0.64 0.27 0.18 22.90 5.09 66.10 0.63 [gray]0.95 Ours (w/ GAN) 4 646 23.63 0.60 0.26 0.17 19.47 4.44 69.30 0.66 4. Experiment Datasets. Following Wang et al. (2024); Dong et al. (2025); Wu et al. (2024a), we use LSDIR (Li et al., 2023) and the first 10K face images from FFHQ (Karras et al., 2019) for training. LR-HR pairs are synthesized with the Real-ESRGAN degradation pipeline (Wang et al., 2021b). We use RealSR (Cai et al., 2019), DRealSR (Wei et al., 2020), and DIV2K-Val (Agustsson and Timofte, 2017) for evaluation, following the same setup as StableSR (Wang et al., 2024). Additionally, we employ a more challenging benchmark constructed by center-cropping 512×512512× 512 patches from the original LSDIR-Val split (Li et al., 2023) to further compare the performance across models. Evaluation Metrics. To verify the performance of different models, we employ structural metrics, perceptual metrics, distribution consistency metrics, and no-reference metrics. Specifically, we report PSNR and SSIM (Wang et al., 2004) (computed on the Y channel of the YCbCr color space) for distortion fidelity, LPIPS (Zhang et al., 2018a) and DISTS (Ding et al., 2020) for perceptual similarity, FID (Heusel et al., 2017) for distribution alignment, and NIQE (Zhang et al., 2015), MUSIQ (Ke et al., 2021), and MANIQA (Yang et al., 2022) as no-reference quality indicators. Implementation Details. We train ScaleResfusion models with SD3 (2B) (Esser et al., 2024), FLUX2-Klein (4B) (Labs, 2025), Z-Image (6B) (Cai et al., 2025), and FLUX2-Klein (9B) as backbones. By default, we use 4-step sampling (we discuss the effects of different sampling steps in the Appendix F.2) and the residual ratio γ=1γ=1 (we discuss the impact of different noise-to-signal ratio initializations in Appendix F.3). We employ RAM-based (Zhang et al., 2024) DAPE following OSEDiff (Wu et al., 2024a) (we discuss the effects of the DAPE in the Appendix F.5). We use a DINOv2-based (Oquab et al., 2023) GAN discriminator identical to AddSR (Xie et al., 2024). Detailed experimental settings are provided in Appendix A.4. Figure 5. Visual comparison with existing diffusion-based restoration methods. The left side shows the result of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Comparison with Existing Methods. Table 1 reports comparisons on RealSR, DRealSR, and DIV2K-Val, with LSDIR results and the full method comparison provided in Appendix D. We compare ScaleResfusion with StableSR (Wang et al., 2024), SUPIR (Yu et al., 2024), CCSR (Sun et al., 2024), OSEDiff (Wu et al., 2024a), ResShift (Yue et al., 2023), and SeeSR (Wu et al., 2024b). These methods cover iterative diffusion models, variants that start diffusion from noisy LQ images, and efficient one-step or few-step generators, providing a representative comparison for Real-IR. Unless otherwise specified, we use the ScaleResfusion built on FLUX2-Klein (4B) as the default model. On DRealSR and RealSR, the w/o GAN variant achieves the best overall performance across PSNR, SSIM, LPIPS, DISTS, and FID; it improves PSNR from 28.24 to 29.77 on DRealSR and from 25.92 to 27.05 on RealSR, while reducing FID from 157.30 to 118.18 on DRealSR and from 122.84 to 104.74 on RealSR. The w/ GAN variant further improves perceptual quality, obtaining the best LPIPS, DISTS, FID, NIQE, and MANIQA on DIV2K-Val and the best NIQE, MUSIQ, and MANIQA on DRealSR and RealSR. This perception–distortion trade-off (Blau and Michaeli, 2018; Zhang et al., 2022b; Luo et al., 2024) is consistent with prior findings (Xie et al., 2024; Yu et al., 2024). Therefore, w/o GAN is preferable for reconstruction fidelity, whereas w/ GAN is better suited for perceptual realism. User Study. User preference evaluation adopts a pairwise Arena design: in each evaluation session, users are presented with results generated by two different models under identical input conditions and make selections based on subjective visual quality and overall preference. The study includes 48 valid independent evaluators and 1,756 comparisons. As shown in Fig. 6, in cross valid comparisons, ScaleResfusion is preferred in 71.8% of cases, compared with 18.4% for baselines and 9.8% for Tie/BothBad. It also achieves a 75.8% overall score in the Random Arena ranking, clearly outperforming all baselines. These results show that ScaleResfusion consistently delivers stronger subjective visual quality and user preference under mixed pairwise comparisons. Figure 6. Pairwise Arena user study results. Left: preference distribution when comparing ScaleResfusion against other methods, where ScaleResfusion wins 71.8% of comparisons. Right: Random Arena ranking, where ScaleResfusion achieves the highest overall score of 75.8%, indicating consistently stronger user preference. Table 2. Ablation results of ScaleResfusion (w/ GAN) on backbone scaling and module design, where the module ablation is conducted on FLUX2-4B. Table (a) presents results on DRealSR, and Table (b) presents results on DIV2K-Val. See the Appendix for the full ablation results. [gray]0.93 (a) Backbone Scaling Backbone Parameters PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ SD3 2B 27.85 0.76 0.32 0.22 146.92 FLUX2 4B 28.26 0.77 0.29 0.20 124.02 ZImage 6B 28.34 0.78 0.28 0.20 127.39 FLUX2 9B 28.77 0.79 0.27 0.19 116.69 [gray]0.93 (b) Module Ablation (on FLUX2-4B) Module PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ Res-init RefNet DMD GAN × ✓ ✓ × 22.60 0.55 0.35 0.23 37.58 ✓ × ✓ × 23.52 0.60 0.28 0.21 23.93 ✓ ✓ × × 21.90 0.51 0.38 0.24 51.25 ✓ ✓ ✓ × 24.90 0.64 0.27 0.18 22.90 ✓ ✓ ✓ ✓ 23.63 0.60 0.26 0.17 19.47 Figure 7. Backbone scaling results of ScaleResfusion in Table 4 (a). Increasing the capacity of the pre-trained rectified-flow backbone consistently improves reconstruction fidelity and distribution alignment, while FLUX2-4B provides the best quality-efficiency trade-off. 5. Ablation Studies Backbone Scaling. Table 4 (a) and Fig. 7 show that ScaleResfusion scales favorably with stronger rectified-flow backbones, consistently improving fidelity, perceptual similarity, and distribution alignment from SD3 (2B) to FLUX2 (9B). This indicates that the proposed residual rectified-flow formulation can effectively inherit richer generative priors from larger pre-trained models rather than being tied to a specific backbone. FLUX2 (9B) achieves the best reconstruction and distribution alignment, while ZImage (6B) obtains the best MUSIQ score, suggesting that different pre-trained priors emphasize different aspects of perceptual quality. FLUX2 (4B) offers the best practical quality-efficiency trade-off, achieving competitive DISTS and FID with much lower inference cost, and is therefore used as our default backbone. More ablation studies are provided in Appendix F. Module Ablation. Table 4 (b) evaluates the key modules on FLUX2 (4B). Removing residual initialization causes the largest fidelity drop, confirming that starting from a residual-aware noisy LQ state is crucial for preserving image structure. Removing RefNet also degrades PSNR, SSIM, and perceptual metrics, showing the importance of injecting LQ reference features during restoration. With Res-init, RefNet, and DMD together, ScaleResfusion achieves the best distortion-oriented performance. Adding GAN further improves perceptual and distribution quality, reducing LPIPS, DISTS, and FID, while introducing the expected perception–distortion trade-off in PSNR and SSIM. 6. Conclusion We presented ScaleResfusion, a scalable Real-IR framework that adapts pre-trained rectified-flow diffusion models through Residual Rectified Flow. By starting from a noisy LQ state and learning a residual vector field, it preserves input structure, retains diffusion sampling, and enables LoRA-based efficient training with knowledge distillation. 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In this zero-shot setting, ScaleResfusion better handles out-of-distribution degradations and restores more natural facial details than competing methods. ScaleResfusion: Residual Rectified Flow based on Residual Vector Field Supplementary Materials Contents AResidual Initialization Leads to a Better Transport Path .. A BAlgorithm .. B CExperimental Setting Details .. C DComparison with Other Methods .. D ECaution on No-Reference Metrics .. E FExtra Ablation Study .. F F.1Ablation on Res-init .. F.1 F.2Ablation on Number of Function Evaluations (NFE) .. F.2 F.3Ablation on Residual Ratio .. F.3 F.4Ablation on DMD Regularization .. F.4 F.5Ablation on DAPE .. F.5 F.6Ablation on Feature Extractor .. F.6 F.7Ablation on LoRA Rank .. F.7 GTheoretical Justification of Residual Rectified Flow .. G HMore Visual Results .. H Appendix A Residual Initialization Leads to a Better Transport Path In this subsection, we provide a theoretical justification for residual initialization from the perspective of measure differential equations. Our key goal is to show that the reverse process induced by the learned residual velocity field is stable with respect to its initial measure. Consequently, in image restoration, an initialization that is closer to the restoration manifold leads to a terminal distribution that is closer to the target HQ distribution. We further show that, conditioned on the observed LQ image, the residual variable R is the most natural task-aware quantity for constructing such a structured initialization. From sample trajectories to measure flows. After the acceleration point t⋆=11+γt = 11+γ, the reverse process of Residual Rectified Flow is governed by the ODE (13) dXtdt=vθ(Xt,t),t∈[0,t⋆], dX_tdt=v_θ(X_t,t), t∈[0,t ], where vθv_θ denotes the learned residual velocity field and Xt⋆X_t is a random initial state. Let μt:=Law(Xt) _t:=Law(X_t) be the probability distribution of XtX_t at time t. Under standard regularity assumptions, the family of measures μtt∈[0,t⋆]\ _t\_t∈[0,t ] satisfies the continuity equation (14) ∂tμt+∇⋅(vθ(⋅,t)μt)=0. _t _t+∇· (v_θ(·,t) _t )=0. Let Φt,s _t,s denote the flow map induced by Eq. (13), namely Xt=Φt,s(Xs).X_t= _t,s(X_s). Then the corresponding measure solution can be written in pushforward form as (15) μt=(Φt,s)#μs. _t=( _t,s)_\# _s. Therefore, the reverse generation process can be interpreted as a measure transport operator t←s(μs):=(Φt,s)#μs,T_t← s( _s):=( _t,s)_\# _s, which transports an initial measure at time s to a terminal measure at time t along the learned residual flow. Stability of the reverse measure flow. To quantify the effect of initialization, consider two initial measures μs _s and νs _s, and let μt=(Φt,s)#μs,νt=(Φt,s)#νs _t=( _t,s)_\# _s, _t=( _t,s)_\# _s be the corresponding evolved measures under the same velocity field vθv_θ. Assume first that vθ(⋅,t)v_θ(·,t) is Lipschitz continuous with respect to the state variable, i.e., there exists a constant L>0L>0 such that (16) ‖vθ(x,t)−vθ(y,t)‖≤L‖x−y‖,∀x,y,∀t∈[0,t⋆].\|v_θ(x,t)-v_θ(y,t)\|≤ L\|x-y\|, ∀ x,y,\ ∀ t∈[0,t ]. Let XtX_t and YtY_t be two characteristic trajectories satisfying dXtdt=vθ(Xt,t),dYtdt=vθ(Yt,t). dX_tdt=v_θ(X_t,t), dY_tdt=v_θ(Y_t,t). Then dt(Xt−Yt)=vθ(Xt,t)−vθ(Yt,t). ddt(X_t-Y_t)=v_θ(X_t,t)-v_θ(Y_t,t). By Eq. (16) and Grönwall’s inequality, we obtain (17) ‖Xt−Yt‖≤eL(t−s)‖Xs−Ys‖.\|X_t-Y_t\|≤ e^L(t-s)\|X_s-Y_s\|. Lifting Eq. (17) to the measure level through an optimal coupling yields the Wasserstein stability estimate (18) W2(μt,νt)≤eL(t−s)W2(μs,νs).W_2( _t, _t)≤ e^L(t-s)W_2( _s, _s). Equation (18) shows that the reverse flow depends continuously on its initial measure. In other words, the discrepancy between terminal distributions is controlled by the discrepancy between their initializations. Non-expansiveness and contraction. Under the standard Lipschitz assumption, Eq. (18) only guarantees that the induced flow operator is eL(t−s)e^L(t-s)-Lipschitz in Wasserstein space. A stronger conclusion can be obtained if the velocity field additionally satisfies the one-sided Lipschitz condition (19) ⟨x−y,vθ(x,t)−vθ(y,t)⟩≤λ‖x−y‖2,∀x,y. x-y,\;v_θ(x,t)-v_θ(y,t) ≤λ\|x-y\|^2, ∀ x,y. In this case, 12dt‖Xt−Yt‖2=⟨Xt−Yt,vθ(Xt,t)−vθ(Yt,t)⟩≤λ‖Xt−Yt‖2, 12 ddt\|X_t-Y_t\|^2= X_t-Y_t,\;v_θ(X_t,t)-v_θ(Y_t,t) ≤λ\|X_t-Y_t\|^2, which implies (20) ‖Xt−Yt‖≤eλ(t−s)‖Xs−Ys‖.\|X_t-Y_t\|≤ e^λ(t-s)\|X_s-Y_s\|. Consequently, at the measure level, (21) W2(μt,νt)≤eλ(t−s)W2(μs,νs).W_2( _t, _t)≤ e^λ(t-s)W_2( _s, _s). Equation (21) leads to the following interpretation: (i) if λ=0λ=0, then W2(μt,νt)≤W2(μs,νs),W_2( _t, _t)≤ W_2( _s, _s), and the reverse flow is non-expansive, i.e., 11-Lipschitz in Wasserstein distance; (i) if λ<0λ<0, then W2(μt,νt)≤eλ(t−s)W2(μs,νs),eλ(t−s)<1,W_2( _t, _t)≤ e^λ(t-s)W_2( _s, _s), e^λ(t-s)<1, and the reverse flow is contractive. Hence, under an additional dissipativity assumption, the learned residual flow not only remains stable but also tends to reduce the discrepancy between different initial measures. Why a structured initialization is preferable. The above stability result shows that the terminal discrepancy of the reverse flow is controlled by the discrepancy of its initialization. Let μt⋆† _t denote an ideal task-aware initial measure, μt⋆G _t ^G a task-agnostic Gaussian initialization, and μt⋆R _t ^R our structured residual initialization. If (22) W2(μt⋆R,μt⋆†)<W2(μt⋆G,μt⋆†),W_2\! ( _t ^R, _t )<W_2\! ( _t ^G, _t ), then the stability estimate in Eq. (18) implies (23) W2(μ0R,μ0†)≤CLW2(μt⋆R,μt⋆†)<CLW2(μt⋆G,μt⋆†),W_2\! ( _0^R, _0 )≤ C_LW_2\! ( _t ^R, _t )<C_LW_2\! ( _t ^G, _t ), where CL=exp(Lt⋆)C_L= (Lt ) and μ0R _0^R, μ0G _0^G, and μ0† _0 are the corresponding terminal measures. Therefore, Eq. (23) should be interpreted as a stability-controlled upper bound rather than an unconditional strict ordering between W2(μ0R,μ0†)W_2( _0^R, _0 ) and W2(μ0G,μ0†)W_2( _0^G, _0 ). It shows that, when the residual initialization is closer to the ideal task-aware initialization at t⋆t , it admits a tighter terminal-discrepancy bound. This provides theoretical motivation for replacing task-agnostic Gaussian initialization with a structured, observation-aware residual initialization. Why the structured variable should be the residual. We now explain why the most natural structured variable for restoration is the residual R. Let x^0 x_0 and x0x_0 denote the LQ and HQ images, respectively, and define (22) R=x^0−x0.R= x_0-x_0. Then (23) x0=x^0−R.x_0= x_0-R. Therefore, conditioned on the observed degraded image x^0 x_0, the target image x0x_0 and the residual variable R are in one-to-one correspondence. Recovering the HQ image is thus equivalent to recovering the residual. In other words, the restoration problem can be reformulated as learning a correction term rather than regenerating the full image from scratch. Moreover, the target velocity in Residual Rectified Flow is (24) ut=γR+ϵ−x0.u_t=γ R+ε-x_0. Substituting Eq. (23) into Eq. (24) yields (25) ut=(γ+1)R+ϵ−x^0.u_t=(γ+1)R+ε- x_0. Equation (25) shows that once the observation x^0 x_0 is given, the task-specific transport direction is primarily governed by the residual variable R. The degraded image x^0 x_0 already provides the coarse structure and semantic layout, while ϵε only maintains the necessary stochasticity. The residual R, in contrast, explicitly captures the correction required to move from the degraded observation to the clean target. Therefore, if one aims to construct an initialization that is closer to the restoration manifold, the residual is the most direct and task-aligned choice. Why residual-only initialization is still insufficient. The above discussion shows that the residual variable R is the most natural task-aware quantity for restoration. However, using only a deterministic residual initialization is still suboptimal. Suppose the initial state is constructed as a deterministic function of the observation, e.g., Xt⋆R-only=g(x^0,R).X_t ^R-only=g( x_0,R). Then, conditioned on x^0 x_0, the induced initial measure degenerates to a Dirac mass: μt⋆R-only(⋅∣x^0)=δg(x^0,R). _t ^R-only(· x_0)= _g( x_0,R). Since the reverse dynamics is governed by a deterministic ODE flow, its pushforward remains a Dirac measure: μ0R-only(⋅∣x^0)=(Φ0,t⋆)#δg(x^0,R)=δΦ0,t⋆(g(x^0,R)). _0^R-only(· x_0)=( _0,t )_\# _g( x_0,R)= _ _0,t (g( x_0,R)). Therefore, a residual-only initialization cannot generate any conditional variability by itself. This property becomes problematic when the target conditional HQ distribution is non-degenerate, i.e., π0(⋅∣x^0) _0(· x_0) has non-zero conditional covariance. In that case, any deterministic terminal measure suffers from an irreducible distribution mismatch. For example, if π0(⋅∣x^0) _0(· x_0) has mean mπm_π and covariance Σπ _π, then W22(δx,π0(⋅∣x^0))=∥x−mπ∥2+Tr(Σπ),W_2^2\! ( _x, _0(· x_0) )=\|x-m_π\|^2+Tr( _π), which is lower bounded by Tr(Σπ)>0Tr( _π)>0 whenever Σπ≠0 _π≠ 0. In contrast, the proposed residual-based initialization preserves task structure while retaining stochastic flexibility: Xt⋆=γ1+γx^0+11+γϵ,ϵ∼(0,I).X_t = γ1+γ x_0+ 11+γε, ε (0,I). Its conditional measure is therefore non-degenerate, μt⋆RN(⋅∣x^0)=(γ1+γx^0,1(1+γ)2I), _t ^RN(· x_0)=N ( γ1+γ x_0,\, 1(1+γ)^2I ), which provides a better balance between structural alignment and distributional coverage. Hence, compared with both task-agnostic Gaussian initialization and purely deterministic residual initialization, the proposed residual-aware noisy initialization is more suitable for restoration-oriented reverse transport. Algorithm 1 Residual Rectified Flow: Main Algorithm Training: Require: Paired LQ-HQ samples (x^0,x0)∼D( x_0,x_0) D, residual ratio γ. t⋆=11+γ [rgb]1,0,0t = 11+γ repeat Sample (x^0i( x_0^i, x0i)∼D,ϵ∼N(0,I)x_0^i) D,ε N(0,I), t∼(0,t⋆)t (0,t ) R=x^0−x0 [rgb]1,0,0R= x_0-x_0 xt=(1−t)x0+tγR+tϵx_t=(1-t)x_0+ [rgb]1,0,0tγ R+tε resv=γR+ϵ−x0 [rgb]1,0,0resv= [rgb]1,0,0γ R+ε-x_0 take gradient step on ∇θ‖resv−resvθ(xt,t)‖2 _θ|| [rgb]1,0,0resv- [rgb]1,0,0resv_θ(x_t,t)||^2 until convergence Inference: Require: LQ image x^0 x_0, residual velocity field resvθresv_θ, residual ratio γ. t⋆=11+γ [rgb]1,0,0t = 11+γ Sample ϵ∼N(0,I)ε N(0,I) xt⋆=t⋆γx0^+t⋆ϵ=γ1+γx^0+11+γϵ [rgb]1,0,0x_t =t γ x_0+t ε= γ1+γ x_0+ 11+γε Solve the ODE dxtdt=resvθ(xt,t) dx_tdt=resv_θ(x_t,t) from t=t⋆t=t to 0 return x0x_0 Implications for ScaleResfusion. The above analysis also explains why residual learning naturally aligns with low-rank parameter-efficient adaptation. In restoration tasks, x^0 x_0 already preserves most of the image content, whereas R mainly contains restoration-specific corrections such as missing high-frequency details, denoising compensation, and deblurring offsets. As a result, the intrinsic complexity of the residual is typically lower than that of the full image signal. This suggests that the dominant task-specific transformation is concentrated in a lower-dimensional residual subspace rather than the entire image space. Consequently, parameter-efficient low-rank adaptation is sufficient to capture the principal residual transport, which provides theoretical support for adopting low-rank updates in ScaleResfusion. In summary, the theoretical justification for residual initialization can be understood from three aspects. First, the reverse process can be formulated as a measure differential equation driven by the learned residual velocity field. Second, the induced measure flow is stable with respect to the initial measure in Wasserstein distance, and becomes non-expansive or even contractive under an additional one-sided Lipschitz condition. Third, conditioned on the LQ observation, the residual variable R is in bijection with the target HQ image and dominates the task-relevant transport direction. Therefore, compared with task-agnostic Gaussian initialization, constructing a structured initial measure from R is better aligned with both the geometry of image restoration and the dynamics of the reverse flow. Appendix B Algorithm Based on the derivations from the Sec 3.3, the training and inference processes of Residual Rectified Flow can be represented as Algorithm 1. We highlight the modifications in our algorithm compared to Standard Rectified Flow in red. Residual Rectified Flow constructs the forward path xt=(1−t)x0+tγR+tϵx_t=(1-t)x_0+tγ R+tε and learns the residual velocity resv=γR+ϵ−x0resv=γ R+ε-x_0 over t∈[0,t⋆]t∈[0,t ], where t⋆=11+γt = 11+γ. During inference, it starts from the acceleration point xt⋆=γ1+γx^0+11+γϵx_t = γ1+γ x_0+ 11+γε and solves the ODE dxtdt=resvθ(xt,t) dx_tdt=resv_θ(x_t,t) from t⋆t to 0 to recover x0x_0. In this way, the reverse process can be interpreted as progressively removing the residual and noise components along the learned continuous trajectory. As formalized in Eq. (5) and Eq. (6), and detailed in Algorithm 1, RRF preserves the Standard Rectified Flow structure and only introduces residual offsets: xt=xtRF+tγRx_t=x_t^RF+tγ R and resv=vRF+γRresv=v^RF+γ R. Therefore, adapting a pre-trained diffusion model to RRF does not require relearning the image-noise transport, but only fitting a compact residual correction. We thus adopt pure LoRA (Hu et al., 2022) as the PEFT strategy, keeping the pre-trained backbone fixed while learning low-rank updates for the residual vector field. Appendix C Experimental Setting Details We train all models with PyTorch and the Diffusers framework following (Hu et al., 2025; Deutch et al., 2024; Liu et al., 2024b; Wang et al., 2025c; Zhang et al., 2025; Zhang and Zhang, 2025), using the AdamW optimizer (Loshchilov and Hutter, 2017) with default hyperparameters. For ScaleResfusion variants using SD3 (2B) and Z-Image (6B) as backbones, we use ReferenceNet to inject LQ features. For variants using FLUX2-Klein (4B, 9B) as backbones, we concatenate the LQ features with the input features along the feature dimension. This preserves the native feature extraction ability of FLUX2 for image editing. We train the SD3 and FLUX2-4B variants on 8 NVIDIA GeForce RTX 5090 GPUs, and the Z-Image and FLUX-9B variants on 8 NVIDIA RTX Pro 6000 GPUs. We train the w/o GAN variant for 100K iterations with a learning rate of 5×10−55× 10^-5, and then fine-tune it with a learning rate of 1×10−51× 10^-5 to obtain w/ GAN. We adopt the Dynamic Distribution Guidance (DynaDG) and Dynamic Renoise Sampling (DynaRS) following Jiang et al. (2025) for cold start during the first 10K iterations. By default, we use 4-step sampling and the residual ratio γ=1γ=1. All testing and inference-time measurements are conducted on a single NVIDIA RTX A6000 GPU. For inference time evaluation, we test all methods at 512×512512× 512 resolution by processing 3,000 images and computing the average inference time per image after subtracting the model loading time from the total time. We employ RAM-based (Zhang et al., 2024) DAPE following OSEDiff (Wu et al., 2024a). We use a DINOv2-based (Oquab et al., 2023) GAN discriminator identical to AddSR (Xie et al., 2024). During training, we also observe a training–inference mismatch similar to the multi-step generator issue discussed in DMD2 (Yin et al., 2024a). In the RRF training process, the x0x_0 component in the observed state xtx_t comes from the real HQ image. During inference, this component must instead be supplied by the generated prediction x0predx_0^pred. With very few (1–4) inference steps, the x0x_0 component changes rapidly between adjacent sampling states, which further amplifies the input-distribution mismatch. This mismatch is less harmful for relatively deterministic restoration tasks such as low-light enhancement and deraining. However, it becomes critical for highly ill-posed problems such as super-resolution, where the generated x0predx_0^pred can deviate substantially from the real x0x_0, leading to over-saturated and hallucinated textures. Following DMD2, we replace noisy real training states with noisy synthetic states produced by the current generator after several sampling steps. Appendix D Comparison with Other Methods Table 3. Full quantitative comparison on real-world benchmarks. Higher is better for PSNR, SSIM, MUSIQ, and MANIQA, while lower is better for LPIPS, DISTS, FID, and NIQE. Methods are grouped into GAN-based, diffusion-based, and ScaleResfusion variants. The best and second-best results of each metric are highlighted in red and blue, respectively. Datasets Type Method PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ NIQE ↓ MUSIQ ↑ MANIQA ↑ BSRGAN 28.70 0.80 0.29 0.21 155.61 6.54 57.15 0.48 Real-ESRGAN 28.61 0.81 0.28 0.21 147.66 6.70 54.27 0.49 LDL 28.20 0.81 0.28 0.21 155.51 7.14 53.94 0.49 GAN-based FeMaSR 26.87 0.76 0.32 0.22 157.72 5.91 53.70 0.44 StableSR 28.04 0.75 0.33 0.23 144.15 6.60 58.53 0.56 SUPIR 25.09 0.65 0.42 0.28 169.48 7.39 58.79 0.55 TSD-SR 27.77 0.76 0.30 0.21 134.98 5.91 66.62 0.59 AddSR 26.68 0.74 0.37 0.26 164.82 7.80 65.36 0.60 CCSR 28.24 0.78 0.32 0.23 157.30 6.81 66.28 0.61 DiffBIR 25.90 0.62 0.47 0.29 180.33 6.33 66.13 0.62 OSEDiff 27.92 0.78 0.30 0.22 135.41 6.46 64.69 0.59 PASD 28.02 0.78 0.32 0.23 174.76 6.72 57.23 0.51 ResShift 27.05 0.74 0.39 0.26 159.90 8.65 51.24 0.47 Diffusion-based SeeSR 28.07 0.77 0.32 0.23 147.37 6.41 65.09 0.61 SD3 (w/o GAN) 28.77 0.79 0.30 0.23 149.67 6.71 63.72 0.60 SD3 (w/ GAN) 27.86 0.76 0.32 0.22 146.93 6.09 64.57 0.61 FLUX2-4B (w/o GAN) 29.77 0.82 0.25 0.20 118.18 6.95 62.42 0.61 FLUX2-4B (w/ GAN) 28.26 0.78 0.29 0.21 124.03 6.21 65.16 0.64 ZImage (w/o GAN) 29.35 0.80 0.28 0.22 132.31 6.78 62.52 0.59 ZImage (w/ GAN) 28.34 0.78 0.28 0.21 127.40 6.16 65.64 0.63 FLUX2-9B (w/o GAN) 30.17 0.82 0.25 0.19 109.28 7.22 60.54 0.59 DRealSR Ours FLUX2-9B (w/ GAN) 28.77 0.79 0.28 0.19 116.69 6.25 62.37 0.62 BSRGAN 26.38 0.77 0.27 0.21 141.24 5.64 63.28 0.54 Real-ESRGAN 26.65 0.76 0.27 0.21 136.29 5.85 60.45 0.55 LDL 25.28 0.76 0.28 0.21 142.74 5.99 60.92 0.55 GAN-based FeMaSR 25.06 0.74 0.29 0.23 141.01 5.77 59.05 0.49 StableSR 24.62 0.70 0.31 0.22 128.54 5.78 65.48 0.62 SUPIR 23.65 0.66 0.35 0.25 130.38 6.11 62.09 0.58 TSD-SR 24.81 0.72 0.27 0.21 114.45 5.13 71.19 0.63 AddSR 22.65 0.65 0.38 0.27 154.18 6.62 71.41 0.67 CCSR 25.92 0.75 0.28 0.21 122.84 5.73 69.18 0.64 DiffBIR 24.83 0.65 0.36 0.24 130.75 5.84 69.28 0.65 OSEDiff 25.15 0.73 0.29 0.21 123.53 5.65 69.08 0.63 PASD 26.04 0.74 0.28 0.21 135.48 5.71 60.03 0.56 ResShift 25.66 0.74 0.33 0.25 128.03 8.07 56.89 0.51 Diffusion-based SeeSR 25.15 0.72 0.30 0.22 125.30 5.40 69.81 0.65 SD3 (w/o GAN) 25.67 0.73 0.29 0.22 126.75 5.96 68.45 0.65 SD3 (w/ GAN) 24.92 0.71 0.30 0.22 126.53 5.61 68.99 0.65 FLUX2-4B (w/o GAN) 27.05 0.78 0.24 0.20 104.74 6.21 67.25 0.64 FLUX2-4B (w/ GAN) 25.78 0.75 0.26 0.20 106.22 5.29 69.86 0.68 ZImage (w/o GAN) 26.29 0.75 0.27 0.21 114.35 5.75 67.33 0.63 ZImage (w/ GAN) 25.44 0.73 0.27 0.21 104.37 5.35 69.25 0.66 FLUX2-9B (w/o GAN) 27.30 0.78 0.23 0.19 96.38 5.94 65.72 0.63 RealSR Ours FLUX2-9B (w/ GAN) 26.12 0.75 0.25 0.18 98.30 5.11 67.64 0.68 Table 4. Full quantitative comparison on synthetic benchmarks. Higher is better for PSNR, SSIM, MUSIQ, and MANIQA, while lower is better for LPIPS, DISTS, FID, and NIQE. Methods are grouped into GAN-based, diffusion-based, and ScaleResfusion variants. The best and second-best results of each metric are highlighted in red and blue, respectively. Datasets Type Method PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ NIQE ↓ MUSIQ ↑ MANIQA ↑ BSRGAN 24.58 0.63 0.35 0.23 49.55 4.75 61.68 0.50 Real-ESRGAN 24.02 0.64 0.32 0.21 38.87 4.83 60.38 0.54 LDL 23.83 0.63 0.33 0.22 42.28 4.86 60.04 0.53 GAN-based FeMaSR 22.45 0.59 0.34 0.22 41.97 4.87 57.94 0.48 StableSR 23.27 0.57 0.31 0.20 24.95 4.77 65.78 0.62 SUPIR 22.13 0.53 0.39 0.23 31.40 5.68 63.86 0.59 TSD-SR 23.02 0.58 0.27 0.18 29.16 4.32 71.69 0.62 AddSR 22.37 0.56 0.38 0.23 34.91 5.84 69.15 0.63 CCSR 24.30 0.63 0.30 0.20 30.84 5.34 69.53 0.61 DiffBIR 23.14 0.54 0.37 0.22 32.71 4.99 69.87 0.64 OSEDiff 23.72 0.61 0.29 0.20 26.34 4.71 67.96 0.61 PASD 24.01 0.61 0.38 0.22 37.06 4.98 63.75 0.55 ResShift 24.59 0.62 0.31 0.21 30.81 6.92 58.90 0.53 Diffusion-based SeeSR 23.68 0.60 0.32 0.20 25.89 4.81 68.66 0.62 SD3 (w/o GAN) 23.90 0.60 0.31 0.21 31.83 4.99 68.66 0.64 SD3 (w/ GAN) 23.13 0.58 0.32 0.20 27.80 4.49 69.89 0.65 FLUX2-4B (w/o GAN) 24.90 0.64 0.27 0.18 22.90 5.09 66.10 0.63 FLUX2-4B (w/ GAN) 23.63 0.60 0.26 0.17 19.47 4.44 69.30 0.68 ZImage (w/o GAN) 23.99 0.62 0.30 0.20 28.55 4.95 67.93 0.63 ZImage (w/ GAN) 23.65 0.60 0.28 0.19 22.96 4.54 69.73 0.65 FLUX2-9B (w/o GAN) 25.18 0.65 0.26 0.18 21.67 5.07 64.89 0.62 DIV2K-Val Ours FLUX2-9B (w/ GAN) 23.97 0.62 0.25 0.16 17.93 4.42 67.50 0.65 BSRGAN 20.82 0.54 0.25 0.16 46.37 4.21 68.94 0.63 Real-ESRGAN 20.58 0.55 0.24 0.15 41.28 4.18 69.52 0.64 LDL 20.31 0.53 0.25 0.16 44.75 4.36 68.61 0.64 GAN-based FeMaSR 19.87 0.51 0.27 0.17 48.63 4.09 67.85 0.61 StableSR 20.31 0.55 0.31 0.18 54.76 5.07 62.96 0.61 SUPIR 20.35 0.50 0.24 0.15 43.81 4.81 71.47 0.67 TSD-SR 19.05 0.49 0.21 0.14 45.66 3.86 74.45 0.68 AddSR 19.20 0.45 0.34 0.20 79.80 4.99 74.20 0.70 CCSR 20.76 0.53 0.26 0.16 56.28 4.25 72.57 0.66 DiffBIR 20.51 0.49 0.27 0.16 58.45 4.44 73.26 0.68 OSEDiff 20.39 0.52 0.27 0.16 59.57 4.03 72.34 0.66 PASD 20.93 0.52 0.31 0.17 59.11 3.80 69.29 0.62 ResShift 21.23 0.55 0.23 0.14 38.98 5.32 68.56 0.61 Diffusion-based SeeSR 20.69 0.52 0.25 0.15 52.06 4.10 73.27 0.68 SD3 (w/o GAN) 20.22 0.52 0.25 0.15 63.84 4.21 74.08 0.70 SD3 (w/ GAN) 19.93 0.51 0.26 0.16 60.61 4.12 73.75 0.70 FLUX2-4B (w/o GAN) 21.35 0.57 0.23 0.14 41.69 4.21 70.61 0.67 FLUX2-4B (w/ GAN) 20.64 0.55 0.21 0.14 43.56 3.82 72.59 0.69 ZImage (w/o GAN) 20.26 0.52 0.23 0.14 54.33 4.17 73.38 0.69 ZImage (w/ GAN) 20.41 0.53 0.24 0.15 51.57 4.07 72.92 0.68 FLUX2-9B (w/o GAN) 21.60 0.57 0.21 0.13 34.43 4.08 69.27 0.66 LSDIR-Val Ours FLUX2-9B (w/ GAN) 20.75 0.55 0.20 0.13 38.34 3.82 72.29 0.70 Table 3 and Table 4 provide the full quantitative comparison on real-world benchmarks (DRealSR and RealSR) and synthetic benchmarks (DIV2K-Val and LSDIR-Val). We compare ScaleResfusion with GAN-based methods, including BSRGAN (Zhang et al., 2021), Real-ESRGAN (Wang et al., 2021b), LDL (Liang et al., 2022), and FeMaSR (Chen et al., 2022), as well as diffusion-based methods, including StableSR (Wang et al., 2024), SUPIR (Yu et al., 2024), TSD-SR (Dong et al., 2025), AddSR (Xie et al., 2024), CCSR (Sun et al., 2024), DiffBIR (Lin et al., 2024), OSEDiff (Wu et al., 2024a), PASD (Yang et al., 2024), ResShift (Yue et al., 2023), and SeeSR (Wu et al., 2024b). These methods cover adversarial restoration models, iterative diffusion models, variants that start diffusion from noisy LQ images, and efficient one-step or few-step generators, providing a broad comparison for Real-IR. We further report ScaleResfusion variants built on SD3 (2B), FLUX2-Klein (4B), Z-Image (6B), and FLUX2-Klein (9B), with and without GAN fine-tuning. We summarize the main observations as follows: (1) On real-world benchmarks, ScaleResfusion achieves the strongest overall fidelity and distribution alignment. On DRealSR, the FLUX2-9B w/o GAN variant reaches 30.17 PSNR, 0.82 SSIM, 0.25 LPIPS, 0.19 DISTS, and 109.28 FID, outperforming existing GAN-based and diffusion-based methods by a clear margin on most reference-based and distribution metrics. On RealSR, the FLUX2-9B w/o GAN variant obtains the best PSNR, SSIM, LPIPS, and FID, while the w/ GAN variant further improves DISTS. These results indicate that the proposed residual rectified-flow formulation does not merely improve perceptual appearance, but also preserves the degraded input content more faithfully than previous restoration-oriented diffusion models. (2) On synthetic benchmarks, ScaleResfusion remains consistently competitive under both DIV2K-Val and LSDIR-Val. On DIV2K-Val, the FLUX2-9B w/o GAN variant achieves the best PSNR and SSIM, while the w/ GAN variant further improves perceptual and distribution metrics, obtaining the best LPIPS, DISTS, and FID. On the more challenging LSDIR-Val benchmark, the FLUX2-9B w/o GAN variant provides the best PSNR, SSIM, FID, and tied-best DISTS, while the w/ GAN variant achieves the best LPIPS and also ties for the best DISTS and MANIQA. In contrast, competing methods usually perform well only on a subset of metrics. For example, some diffusion-based methods obtain strong no-reference scores but suffer from weaker distortion fidelity, whereas GAN-based methods can preserve local structure but often show inferior distribution alignment. (3) ScaleResfusion variants with and without GAN fine-tuning exhibit a clear perception–distortion trade-off. The w/o GAN variant is generally better for reconstruction fidelity, as reflected by higher PSNR/SSIM and strong LPIPS/DISTS on paired benchmarks. The w/ GAN variant tends to improve no-reference quality and perceptual realism, especially on MANIQA, NIQE, and MUSIQ, at the cost of a moderate decrease in pixel-level fidelity. Table 1 shows this trend clearly for FLUX2-4B: adding GAN fine-tuning improves NIQE/MUSIQ/MANIQA from 6.95/62.42/0.61 to 6.21/65.16/0.64 on DRealSR, from 6.21/67.25/0.64 to 5.29/69.86/0.68 on RealSR, and from 5.09/66.10/0.63 to 4.44/69.30/0.66 on DIV2K-Val. Meanwhile, the same fine-tuning decreases PSNR/SSIM from 29.77/0.82 to 28.26/0.78 on DRealSR, from 27.05/0.78 to 25.78/0.75 on RealSR, and from 24.90/0.64 to 23.63/0.60 on DIV2K-Val. This behavior is consistent with the known perception–distortion trade-off in image restoration and also explains why we report both variants: users can select the more faithful or more perceptual model depending on the target application. (4) Stronger rectified-flow backbones further improve the robustness of ScaleResfusion. Across DRealSR, RealSR, DIV2K-Val, and LSDIR-Val, FLUX2-9B generally provides the best or second-best results among our variants. Although FLUX2-4B is not the strongest variant, it offers a practical performance-efficiency trade-off by maintaining competitive restoration quality while achieving sub-second inference. This scaling trend supports the central motivation of ScaleResfusion: by formulating restoration as residual rectified-flow adaptation, large pre-trained generative priors can be effectively reused for real-world image restoration with only task-specific residual updates. Figure 10. No-reference metric comparison on examples without ground truth. Although TSD-SR still obtains better MUSIQ/NIQE scores than ScaleResfusion, its visual quality is clearly worse, with stronger semantic drift and local artifacts. Visual comparison between TSD-SR and ScaleResfusion on examples without ground truth, showing that better no-reference scores can still correspond to worse visual quality. Figure 11. Examples where no-reference metrics do not fully reflect visual quality. TSD-SR obtains higher MUSIQ/MANIQA scores, but introduces stronger artifacts and less faithful structures than ScaleResfusion. Visual comparison between TSD-SR, ScaleResfusion, and ground truth, showing that higher no-reference scores can correspond to worse visual fidelity. Appendix E Caution on No-Reference Metrics No-reference metrics are useful when ground-truth images are unavailable, but current metrics still contain biases toward certain low-level statistics, such as sharpness, contrast, and texture richness. As a result, they may assign higher scores to images with over-sharpened details, semantic drift, or local artifacts, even when these artifacts reduce restoration fidelity. Fig. 11 shows paired examples where TSD-SR obtains higher MUSIQ/MANIQA scores than ScaleResfusion, yet its outputs have lower reference fidelity and visibly stronger artifacts. This indicates that no-reference scores can be inconsistent with both ground-truth-based metrics and human visual judgment. Fig. 10 further considers examples without ground-truth images, where reference-based metrics such as PSNR/SSIM cannot be computed and evaluation naturally relies more on no-reference scores. Although TSD-SR reports better no-reference scores in these cases, the visual comparison reveals facial semantic drift, unstable exposure and color appearance, and structural degradation. ScaleResfusion better preserves plausible structures and overall appearance, suggesting that the bias of no-reference metrics can become more visible when they are used in isolation. Together with the paired examples in Fig. 11, this motivates a more balanced evaluation protocol: when the gap in no-reference metrics is not substantial, consistency-oriented metrics (PSNR, SSIM, LPIPS, DISTS) and distribution-level metrics (FID) should receive more weight whenever they are available, since they better capture whether the restored image remains faithful to the input content and aligned with the target image distribution. We thus treat no-reference scores as complementary indicators rather than the sole criterion for evaluating Real-IR quality. Appendix F Extra Ablation Study In this section, we provide additional ablation studies to analyze the effects of sampling steps, residual ratio, residual initialization, DMD, GAN fine-tuning, DAPE, feature extraction, and LoRA rank. We follow the same evaluation protocol as the main experiments and use the FLUX2-4B variant as the default setting unless otherwise specified. Figure 12. Visual ablation on residual initialization. Compared with task-agnostic Gaussian initialization, residual initialization starts from a more restoration-aligned state and better preserves the observed image structure. Visual comparison between Gaussian initialization and residual initialization. Figure 13. Intermediate restoration results from the same multi-step model. As the number of function evaluations (NFE) increases during sampling, ScaleResfusion progressively updates the residual state, leading to clearer structures and more refined image details. Intermediate ScaleResfusion restoration results showing that image details are progressively refined as the number of function evaluations increases. Table 5. Ablation on residual initialization strategies under SD3 and FLUX2-4B on DRealSR and LSDIR-Val. Dataset Backbone Res-init PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR SD3 Gaussian init 26.92 0.70 0.34 165.20 DRealSR SD3 Res-init 28.77 0.79 0.30 149.67 DRealSR FLUX2-4B Gaussian init 26.83 0.72 0.35 137.58 DRealSR FLUX2-4B Res-init 29.77 0.82 0.25 118.18 LSDIR-Val SD3 Gaussian init 17.87 0.41 0.29 79.37 LSDIR-Val SD3 Res-init 20.22 0.52 0.25 63.84 LSDIR-Val FLUX2-4B Gaussian init 19.69 0.46 0.39 61.09 LSDIR-Val FLUX2-4B Res-init 21.35 0.57 0.23 41.69 Table 6. Ablation on the number of function evaluations (NFE). We compare 4-step, 2-step, and 1-step sampling under two backbones on DRealSR and LSDIR-Val. Dataset Backbone NFE PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR SD3 4-step 28.77 0.79 0.30 149.67 DRealSR SD3 2-step 28.61 0.78 0.31 150.90 DRealSR SD3 1-step 28.23 0.77 0.31 153.65 DRealSR FLUX2-4B 4-step 29.77 0.82 0.25 118.18 DRealSR FLUX2-4B 2-step 29.03 0.79 0.27 115.43 DRealSR FLUX2-4B 1-step 28.93 0.78 0.28 117.56 LSDIR-Val SD3 4-step 20.22 0.52 0.25 63.84 LSDIR-Val SD3 2-step 19.56 0.49 0.26 65.07 LSDIR-Val SD3 1-step 19.18 0.48 0.26 67.82 LSDIR-Val FLUX2-4B 4-step 21.35 0.57 0.23 41.69 LSDIR-Val FLUX2-4B 2-step 20.61 0.54 0.25 38.94 LSDIR-Val FLUX2-4B 1-step 20.51 0.53 0.26 41.07 Figure 14. Visual ablation on the number of function evaluations. Increasing the number of sampling steps generally improves restoration fidelity and detail consistency, while the proposed residual transport remains effective even with very few steps. Visual comparison of ScaleResfusion restoration results under different numbers of function evaluations. F.1. Ablation on Res-init The main purpose of this ablation is to verify the effectiveness of Residual Rectified Flow (RRF). To isolate the effect of the RRF formulation, we train a baseline with the same backbone, data, optimizer, and knowledge-distillation based training pipeline as ScaleResfusion, but replace the RRF starting state with task-agnostic Gaussian noise. Therefore, the comparison in Table 5 and Fig. 12 directly examines whether starting from a noisy LQ-related residual state is more suitable for restoration than starting from Gaussian noise. As shown in Table 5, residual initialization substantially improves restoration fidelity for both backbones. On DRealSR, it increases SD3 from 26.92 to 28.77 PSNR and from 0.70 to 0.79 SSIM. On FLUX2-4B, PSNR increases from 26.83 to 29.77 and SSIM increases from 0.72 to 0.82. LSDIR-Val shows the same pattern: residual initialization improves SD3 from 17.87 to 20.22 PSNR and from 0.41 to 0.52 SSIM, and improves FLUX2-4B from 19.69 to 21.35 PSNR and from 0.46 to 0.57 SSIM. Residual initialization also improves perceptual and distribution metrics. Compared with Gaussian initialization on DRealSR, it reduces LPIPS from 0.34 to 0.30 and FID from 165.20 to 149.67 on SD3, and reduces LPIPS from 0.35 to 0.25 and FID from 137.58 to 118.18 on FLUX2-4B. On LSDIR-Val, it reduces LPIPS from 0.29 to 0.25 and FID from 79.37 to 63.84 on SD3, and reduces LPIPS from 0.39 to 0.23 and FID from 61.09 to 41.69 on FLUX2-4B. These results directly support the motivation of RRF. Starting from a noisy LQ-related state is better aligned with the restoration task, because the initial state already preserves the observed structure and the model only needs to transport residual corrections toward the HQ image. In contrast, the Gaussian-initialized baseline must synthesize both global structure and restoration details from a task-agnostic noise state, which makes few-step restoration much harder even under the same distillation pipeline. F.2. Ablation on Number of Function Evaluations (NFE) We study the effect of sampling steps by training separate 1-step, 2-step, and 4-step models under the same knowledge-distillation based training pipeline. This controlled setting evaluates how the target number of function evaluations affects models that are explicitly trained for different inference budgets. As shown in Table 6, more sampling steps generally improve reconstruction fidelity across both SD3 and FLUX2-4B. The 4-step setting gives the most stable distortion and perceptual similarity metrics on DRealSR and LSDIR-Val, so we use it as the default configuration. Meanwhile, the 1-step and 2-step variants remain competitive, indicating that the RRF acceleration point provides a strong initialization for fast restoration. Beyond comparing separately trained models, Fig. 13 visualizes the intermediate predictions of the same multi-step model during sampling. Early evaluations recover the main image structure, while later evaluations progressively correct detail-level errors, reduce local inconsistencies, and refine high-frequency textures. This shows that the multi-step trajectory is not redundant: additional function evaluations allow ScaleResfusion to iteratively polish residual artifacts and improve local consistency. Figure 15. Visual ablation on the residual ratio γ. The residual ratio controls the balance between deterministic LQ guidance and stochastic restoration, leading to different fidelity–realism trade-offs. Visual comparison of ScaleResfusion restoration results under different residual ratios. Table 7. Ablation on the residual ratio γ. We evaluate three residual ratios under two backbones on DRealSR and LSDIR-Val. Dataset Backbone γ PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR SD3 2.0 29.53 0.81 0.27 139.44 DRealSR SD3 1.0 28.77 0.79 0.30 149.67 DRealSR SD3 0.5 28.64 0.78 0.30 148.19 DRealSR FLUX2-4B 2.0 30.49 0.83 0.26 120.03 DRealSR FLUX2-4B 1.0 29.77 0.82 0.25 118.18 DRealSR FLUX2-4B 0.5 29.18 0.79 0.28 132.45 LSDIR-Val SD3 2.0 20.48 0.52 0.22 53.61 LSDIR-Val SD3 1.0 20.22 0.52 0.25 63.84 LSDIR-Val SD3 0.5 19.59 0.49 0.25 62.36 LSDIR-Val FLUX2-4B 2.0 22.07 0.58 0.24 43.54 LSDIR-Val FLUX2-4B 1.0 21.35 0.57 0.23 41.69 LSDIR-Val FLUX2-4B 0.5 20.76 0.54 0.26 55.96 Table 8. Ablation on DMD with the FLUX2-4B backbone. Res-init and RefNet are enabled for both variants, and GAN fine-tuning is disabled. DMD PSNR ↑ SSIM ↑ LPIPS ↓ DISTS ↓ FID ↓ × 21.90 0.51 0.38 0.24 51.25 ✓ 24.90 0.64 0.27 0.18 22.90 F.3. Ablation on Residual Ratio We further ablate the residual ratio γ introduced in Sec. 3.3. As discussed in Sec. 3.3, γ directly determines the signal-to-noise ratio (SNR) of the RRF acceleration point: a larger γ makes the initial state closer to the LQ-related residual signal, while a smaller γ injects stronger Gaussian randomness. This parameter therefore controls how much the sampling process relies on deterministic LQ initialization versus stochastic generative refinement. Table 7 shows that increasing γ generally improves fidelity-oriented metrics. For example, moving from γ=0.5γ=0.5 to γ=2.0γ=2.0 consistently improves PSNR and SSIM on both DRealSR and LSDIR-Val, suggesting that a stronger residual signal helps preserve the observed image structure. The visual comparison in Fig. 15 follows the same trend: small γ values leave more room for stochastic restoration but can introduce unstable details, while larger γ values raise the SNR of the starting state and therefore provide stronger structural guidance. However, the largest γ is not always the best choice for perceptual and distribution-level quality. On FLUX2-4B, γ=1.0γ=1.0 achieves better LPIPS and FID than γ=2.0γ=2.0 on both evaluated datasets, indicating that excessive reliance on the LQ-related signal may improve pixel fidelity while limiting realistic detail synthesis and distribution alignment. We therefore use γ=1.0γ=1.0 by default, as it preserves sufficient input structure while retaining enough stochasticity for realistic restoration. Figure 16. Visual ablation on GAN fine-tuning. GAN fine-tuning enhances perceptual sharpness and local details, while occasionally reducing content consistency with the input or reference. Visual comparison of restoration results with and without GAN fine-tuning. Figure 17. Visual ablation on DMD. DMD reduces the training-inference mismatch of the few-step generator and improves both structural fidelity and perceptual detail quality. Visual comparison of restoration results with and without DMD. F.4. Ablation on DMD Regularization We further analyze the effect of DMD regularization using FLUX2-4B as the base model. As described in Sec. 3.4, the DMD term transfers the natural-image prior of the frozen pre-trained diffusion model to the few-step RRF generator through a teacher-student distribution-matching objective. This is especially important for ScaleResfusion because the generator is trained to produce high-quality restorations in only a few sampling steps, where small distribution errors can quickly accumulate into artifacts or structure drift. To isolate the effect of DMD, we keep residual initialization and LQ conditioning enabled, while disabling GAN fine-tuning. Table 8 shows that DMD is crucial for stable few-step restoration. Without DMD, the FLUX2-4B variant obtains only 21.90 PSNR, 0.51 SSIM, 0.38 LPIPS, 0.24 DISTS, and 51.25 FID. Adding DMD improves PSNR to 24.90 and SSIM to 0.64, while reducing LPIPS to 0.27, DISTS to 0.18, and FID to 22.90. The visual results in Fig. 17 show the same tendency: DMD suppresses unstable textures and improves structural fidelity. These results indicate that DMD regularization alleviates the mismatch between supervised training states and inference-time generated states, allowing the few-step generator to stay closer to the HQ image manifold and produce more faithful and realistic outputs. Figure 18. Visual ablation on DAPE. Replacing DAPE with a fixed prompt simplifies the pipeline but loses image-specific semantic and degradation-aware guidance, while DAPE better preserves structures and degradation-specific details. Visual comparison between fixed-prompt conditioning and DAPE, showing the effect of image-specific textual guidance. Table 9. Ablation on replacing DAPE with a fixed prompt using the FLUX2-4B backbone on DRealSR and LSDIR-Val. Dataset Variant PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR Fixed prompt 28.39 0.78 0.28 130.98 DRealSR DAPE 29.77 0.82 0.25 118.18 LSDIR-Val Fixed prompt 20.83 0.55 0.23 47.95 LSDIR-Val DAPE 21.35 0.57 0.23 41.69 Figure 19. Visual ablation on LQ feature conditioning. Removing LQ conditioning allows the model to synthesize more diverse details, but it also weakens input consistency and reconstruction fidelity. Visual comparison of restoration results with and without LQ feature conditioning, showing the trade-off between detail diversity and input fidelity. F.5. Ablation on DAPE We analyze whether the image-specific semantic information provided by DAPE can be replaced by a fixed restoration prompt, which would remove the extra DAPE module and simplify inference. This is a practical trade-off: the pre-trained models inherently possess strong feature extraction capabilities, so a fixed prompt may be sufficient for many cases. Table 9 and Fig. 18 show that the fixed-prompt variant is not invalid; it still produces reasonable restoration results under the same FLUX2-4B backbone. However, DAPE consistently improves PSNR, SSIM, LPIPS, and FID on DRealSR, and also improves PSNR, SSIM, and FID on LSDIR-Val. The visual comparison further suggests that image-specific textual guidance helps recover more faithful structures and degradation-specific details. Therefore, replacing DAPE with a fixed prompt is a viable lightweight option when simplicity is preferred, but the default DAPE setting offers a better quality–robustness trade-off. Figure 20. Visual ablation on the number of feature extractor layers. Using more feature extraction layers provides stronger LQ conditioning and improves fine-detail restoration. Visual comparison of restoration results using different numbers of LoRA-branch feature extractor layers. Figure 21. Visual ablation on LoRA rank. Increasing the LoRA rank gives the residual generator more adaptation capacity and improves perceptual detail quality. Visual comparison of restoration results using different LoRA ranks. Table 10. Ablation on using the feature extractor on DRealSR and LSDIR-Val. Dataset Variant PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR w/o Ref. Attention 28.93 0.79 0.28 129.86 DRealSR w/ Ref. Attention 29.77 0.82 0.25 118.18 LSDIR-Val w/o Ref. Attention 20.51 0.54 0.26 53.37 LSDIR-Val w/ Ref. Attention 21.35 0.57 0.23 41.69 F.6. Ablation on Feature Extractor Effect of LQ Feature Conditioning. We compare ScaleResfusion with and without the feature extractor. The feature extractor provides explicit LQ feature injection as an additional conditioning signal, helping the generator align restored structures with the degraded input. Removing this conditioning gives the generative prior more freedom to synthesize diverse details, but it also weakens the constraint from the observation, which may reduce fidelity and input consistency. Table 10 shows this trade-off quantitatively. Adding Ref. Attention improves PSNR from 28.93 to 29.77 and SSIM from 0.79 to 0.82 on DRealSR, and improves PSNR from 20.51 to 21.35 and SSIM from 0.54 to 0.57 on LSDIR-Val. The same setting also reduces LPIPS and FID on both datasets, suggesting that LQ feature conditioning improves not only distortion fidelity but also perceptual and distribution-level quality. The visual comparison in Fig. 19 further illustrates the role of the feature extractor. Without LQ conditioning, the model can generate richer or more varied local details, but these details are less tightly anchored to the input image and can deviate from the original structure. With feature extraction, ScaleResfusion better preserves the observed content while still benefiting from the generative prior, leading to a more reliable fidelity–diversity trade-off. Layers of Feature Extractor. We further ablate the number of LoRA-branch feature extractor layers on SD3 to study how much LQ information should be injected into the residual generator. As shown in Table 11, using more feature extractor layers consistently improves restoration quality. Increasing the number of layers from 4 to 23 improves PSNR/SSIM and reduces LPIPS/FID on both DRealSR and LSDIR-Val, indicating that deeper feature extraction provides more complete conditioning. This trend is consistent with the role of LQ feature injection. Shallow feature settings mainly provide coarse structural cues, which help anchor the global layout but are less effective at transferring fine textures, local degradation patterns, and high-frequency details. Deeper settings expose the residual generator to richer multi-level LQ representations, allowing it to better preserve input content while producing natural HQ details. We therefore use the full 23-layer feature extractor for SD3, as it provides the strongest and most complete conditioning signal. Table 11. Ablation on the number of feature extractor layers with SD3 backbone on DRealSR and LSDIR-Val. Dataset # Layers PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR 23 28.77 0.79 0.30 149.67 DRealSR 16 28.41 0.78 0.31 153.82 DRealSR 8 28.02 0.76 0.33 161.35 DRealSR 4 27.68 0.75 0.35 168.90 LSDIR-Val 23 20.22 0.52 0.25 63.84 LSDIR-Val 16 19.36 0.49 0.26 67.99 LSDIR-Val 8 18.97 0.47 0.28 75.52 LSDIR-Val 4 18.63 0.46 0.30 83.07 Table 12. Ablation on LoRA rank on DRealSR and LSDIR-Val. Dataset Rank PSNR ↑ SSIM ↑ LPIPS ↓ FID ↓ DRealSR 32 29.77 0.82 0.25 118.18 DRealSR 16 29.42 0.80 0.26 123.64 DRealSR 8 29.05 0.79 0.28 131.37 DRealSR 4 28.63 0.77 0.30 140.82 LSDIR-Val 32 21.35 0.57 0.23 41.69 LSDIR-Val 16 21.00 0.55 0.24 47.15 LSDIR-Val 8 20.63 0.54 0.26 54.88 LSDIR-Val 4 20.21 0.52 0.28 64.33 F.7. Ablation on LoRA Rank Finally, we ablate the LoRA rank, which controls the capacity of the trainable residual update while keeping the pre-trained backbone frozen. Since ScaleResfusion only learns low-rank updates for the residual vector field, the rank determines how expressive this residual adaptation subspace can be. A very small rank may be sufficient for coarse task adaptation, but it can underfit structured high-frequency corrections that are important for faithful restoration. Table 12 shows a consistent improvement as the rank increases. On DRealSR, increasing the rank from 4 to 32 improves PSNR and SSIM while reducing LPIPS and FID. LSDIR-Val follows the same trend, with higher rank providing better fidelity and stronger distribution alignment. Notably, even rank 4 already achieves reasonable restoration quality, which supports the residual formulation in Sec. 3.3: the residual vector field differs from the standard Rectified Flow target only by a residual offset, so the adaptation does not need to relearn the full image-noise transport from scratch. This indicates that ScaleResfusion can make effective use of a compact LoRA subspace. Rank 32 provides the best overall performance in our setting. At the same time, the stable trend across ranks supports our design choice: ScaleResfusion can adapt a large pre-trained backbone through a compact LoRA subspace, and increasing the subspace capacity further helps capture the structured residual corrections required by Real-IR. Appendix G Theoretical Justification of Residual Rectified Flow We justify Residual Rectified Flow (RRF) by following the marginal-preserving argument of nonlinear Rectified Flow (Liu et al., 2022). Different from the canonical Rectified Flow, which constructs a linear interpolation between two endpoint distributions, our residual construction defines an observation-dependent stochastic path whose intermediate state admits an exact acceleration point. Therefore, RRF inherits the marginal-preserving property of nonlinear Rectified Flow, while its acceleration point comes from clean-image coefficient cancellation in the residual parameterization. Let X0∈ℝdX_0 ^d denote the clean high-quality image and let C=X^0∈ℝdC= X_0 ^d denote the image-space condition obtained from the low-quality observation, such as an upsampled or preliminary restored image. Let ϵ∼(0,Σ)ε (0, ) be independent Gaussian noise. For a fixed residual strength γ>0γ>0, define the residual endpoint (26) Yγ=γ(C−X0)+ϵ.Y_γ=γ(C-X_0)+ε. We then construct the residual interpolation (27) Xt=(1−t)X0+tYγ,t∈[0,1].X_t=(1-t)X_0+tY_γ, t∈[0,1]. Equivalently, (28) Xt=(1−t)X0+tγ(C−X0)+tϵ,X_t=(1-t)X_0+tγ(C-X_0)+tε, and hence (29) Xt=[1−(1+γ)t]X0+γtC+tϵ.X_t=[1-(1+γ)t]X_0+γ tC+tε. The pathwise velocity is (30) X˙t=Yγ−X0=γ(C−X0)+ϵ−X0. X_t=Y_γ-X_0=γ(C-X_0)+ε-X_0. We denote Ut:=X˙tU_t:= X_t. Following Definition 3.1 of original Rectified Flow (Liu et al., 2022), which defines the expected velocity as vX(x,t)=[X˙t∣Xt=x]v^X(x,t)=E[ X_t X_t=x] for a pathwise differentiable process, we define the conditional expected velocity by (31) vX(x,t,c)=[X˙t∣Xt=x,C=c].v^X(x,t,c)=E[ X_t X_t=x,C=c]. In practice, vXv^X is approximated by a neural network vθ(x,t,c)v_θ(x,t,c). Following Eq. (6) of original Rectified Flow (Liu et al., 2022), which fits the nonlinear Rectified Flow velocity by matching v(Xt,t)v(X_t,t) to X˙t X_t, we use the least-squares objective (32) minθ∫01[‖vθ(Xt,t,C)−X˙t‖22]t. _θ _0^1E [ \|v_θ(X_t,t,C)- X_t \|_2^2 ]dt. Here we take the weight wt=1w_t=1 in Eq. (6) of original Rectified Flow (Liu et al., 2022) and add the condition C as input. Equivalently, (33) minθ∫01[‖vθ(Xt,t,C)−(γ(C−X0)+ϵ−X0)‖22]t. _θ _0^1E [ \|v_θ(X_t,t,C)- (γ(C-X_0)+ε-X_0 ) \|_2^2 ]dt. Definition 1: Conditional residual rectified flow. For each fixed condition C=cC=c, define (34) Xtc=[1−(1+γ)t]X0+γtc+tϵ.X_t^c=[1-(1+γ)t]X_0+γ tc+tε. Its expected velocity is (35) vX(x,t,c)=[X˙t∣Xt=x,C=c].v^X(x,t,c)=E[ X_t X_t=x,C=c]. We call X=Xt:t∈[0,1]X=\X_t:t∈[0,1]\ conditionally rectifiable if vX(⋅,t,c)v^X(·,t,c) is locally bounded and the integral equation (36) Zt=Z0+∫0tvX(Zs,s,c)sZ_t=Z_0+ _0^tv^X(Z_s,s,c)\,ds admits a unique solution for each fixed c. Following Eq. (9) of original Rectified Flow (Liu et al., 2022), where the rectified flow is defined by the integral equation driven by vXv^X, the above equation is its conditional counterpart after fixing C=cC=c. Theorem 1: Conditional marginal preservation. Assume that, for each fixed C=cC=c, the residual interpolation XtX_t is conditionally rectifiable. Let ZtZ_t solve (37) dZt=vX(Zt,t,c)dt,Z0∣C=c∼X0∣C=c.dZ_t=v^X(Z_t,t,c)\,dt, Z_0 C=c X_0 C=c. Then (38) Law(Zt∣C=c)=Law(Xt∣C=c),∀t∈[0,1].Law(Z_t C=c)=Law(X_t C=c), ∀ t∈[0,1]. Proof. Fix C=cC=c. The proof is the conditional version of Theorem 3.3 in (Liu et al., 2022). Let πtc:=Law(Xt∣C=c) _t^c:=Law(X_t C=c). Following Eq. (10) of original Rectified Flow (Liu et al., 2022), for any compactly supported continuously differentiable test function h:ℝd→ℝh:R^d , the chain rule gives (39) dt[h(Xt)∣C=c]=[∇h(Xt)⊤X˙t∣C=c]. ddtE[h(X_t) C=c]=E[∇ h(X_t) X_t C=c]. Following the conditional expected-velocity substitution in Eq. (10) of original Rectified Flow (Liu et al., 2022), we use (40) vX(Xt,t,c)=[X˙t∣Xt,C=c],v^X(X_t,t,c)=E[ X_t X_t,C=c], and obtain (41) [∇h(Xt)⊤X˙t∣C=c]=[∇h(Xt)⊤vX(Xt,t,c)∣C=c].E[∇ h(X_t) X_t C=c]=E[∇ h(X_t) v^X(X_t,t,c) C=c]. This is Eq. (10) of original Rectified Flow (Liu et al., 2022) with the unconditional velocity vX(Xt,t)v^X(X_t,t) replaced by the conditional velocity vX(Xt,t,c)v^X(X_t,t,c). Therefore, (42) dt[h(Xt)∣C=c]=[∇h(Xt)⊤vX(Xt,t,c)∣C=c]. ddtE[h(X_t) C=c]=E[∇ h(X_t) v^X(X_t,t,c) C=c]. Following Eq. (11) of original Rectified Flow (Liu et al., 2022), the above weak identity is equivalently written as the continuity equation for πtc _t^c in the sense of distributions: (43) π˙tc+∇⋅(vX(⋅,t,c)πtc)=0. π_t^c+∇· (v^X(·,t,c) _t^c )=0. Following the paragraph below Eq. (11) of original Rectified Flow (Liu et al., 2022), this weak equivalence follows by multiplying the continuity equation by h and integrating by parts. Since ZtZ_t is driven by the same velocity field vX(⋅,t,c)v^X(·,t,c), its conditional law qtc:=Law(Zt∣C=c)q_t^c:=Law(Z_t C=c) also satisfies (44) q˙tc+∇⋅(vX(⋅,t,c)qtc)=0. q_t^c+∇· (v^X(·,t,c)q_t^c )=0. Moreover, q0c=π0cq_0^c= _0^c by the initialization assumption. By the uniqueness of the weak solution to the continuity equation, we obtain (45) qtc=πtc,∀t∈[0,1].q_t^c= _t^c, ∀ t∈[0,1]. Thus, (46) Law(Zt∣C=c)=Law(Xt∣C=c).Law(Z_t C=c)=Law(X_t C=c). This proves the claim. Following Theorem 3.3 of original Rectified Flow (Liu et al., 2022), the stochastic interpolation XtX_t and the deterministic ODE ZtZ_t solve the same continuity equation in Eq. (11), so their one-time marginals coincide. Theorem 2: Exact acceleration point. For the residual interpolation (47) Xt=[1−(1+γ)t]X0+γtC+tϵ,X_t=[1-(1+γ)t]X_0+γ tC+tε, there exists a unique time (48) t⋆=11+γt = 11+γ at which the clean-image component X0X_0 is exactly cancelled. At this time, (49) Xt⋆=γ1+γC+11+γϵ.X_t = γ1+γC+ 11+γε. Proof. The coefficient of X0X_0 in XtX_t is 1−(1+γ)t1-(1+γ)t. Setting this coefficient to zero gives (50) 1−(1+γ)t⋆=0.1-(1+γ)t =0. Therefore, (51) t⋆=11+γ.t = 11+γ. Substituting t⋆t into the residual interpolation gives (52) Xt⋆=[1−(1+γ)t⋆]X0+γt⋆C+t⋆ϵ.X_t =[1-(1+γ)t ]X_0+γ t C+t ε. Since 1−(1+γ)t⋆=01-(1+γ)t =0, we have (53) Xt⋆=γt⋆C+t⋆ϵ.X_t =γ t C+t ε. Using t⋆=1/(1+γ)t =1/(1+γ), we obtain (54) Xt⋆=γ1+γC+11+γϵ.X_t = γ1+γC+ 11+γε. Thus, Xt⋆X_t depends only on the condition C and Gaussian noise ϵε, but not on the unknown clean image X0X_0. If ϵ∼(0,Σ)ε (0, ), then (55) Xt⋆∣C=c∼(γ1+γc,1(1+γ)2Σ).X_t C=c ( γ1+γc, 1(1+γ)^2 ). Hence, the reverse ODE can be initialized from (56) Zt⋆=γ1+γC+11+γϵ,ϵ∼(0,Σ).Z_t = γ1+γC+ 11+γε, ε (0, ). By Theorem 1, under the population velocity field and exact ODE integration, (57) Z0∣C=c∼X0∣C=c.Z_0 C=c X_0 C=c. Training objective of RRF. Since (58) X˙t=γ(C−X0)+ϵ−X0, X_t=γ(C-X_0)+ε-X_0, the population RRF objective is obtained by following Eq. (6) of original Rectified Flow (Liu et al., 2022) and substituting the residual path velocity X˙t=γ(C−X0)+ϵ−X0 X_t=γ(C-X_0)+ε-X_0: (59) ℒRRF(θ)=∫01[‖vθ(Xt,t,C)−(γ(C−X0)+ϵ−X0)‖22]t.L_RRF(θ)= _0^1E [ \|v_θ(X_t,t,C)- (γ(C-X_0)+ε-X_0 ) \|_2^2 ]dt. Equivalently, if training is restricted to the accelerated interval [0,t⋆][0,t ], one may use (60) ℒRRF(θ)=∫0t⋆[‖vθ(Xt,t,C)−(γ(C−X0)+ϵ−X0)‖22]t.L_RRF(θ)= _0^t E [ \|v_θ(X_t,t,C)- (γ(C-X_0)+ε-X_0 ) \|_2^2 ]dt. Following Eq. (2) of original Rectified Flow (Liu et al., 2022), where the canonical population minimizer is vX(x,t)=[X1−X0∣Xt=x]v^X(x,t)=E[X_1-X_0 X_t=x], the RRF population minimizer is (61) v⋆(x,t,c)=[γ(C−X0)+ϵ−X0∣Xt=x,C=c].v (x,t,c)=E[γ(C-X_0)+ε-X_0 X_t=x,C=c]. Relation to Rectified Flow. RRF preserves the linear transport form of standard Rectified Flow. Recall that canonical Rectified Flow constructs the straight interpolation (62) Xt=(1−t)X0+tX1X_t=(1-t)X_0+tX_1 and learns the velocity field associated with the path derivative X1−X0X_1-X_0. In RRF, we replace the standard endpoint X1X_1 with the residual endpoint (63) Yγ=γ(C−X0)+ϵ,Y_γ=γ(C-X_0)+ε, which gives (64) Xt=(1−t)X0+tYγ.X_t=(1-t)X_0+tY_γ. Therefore, conditioned on C, RRF is still a linear interpolation between two endpoints, and its pathwise velocity is (65) X˙t=Yγ−X0=γ(C−X0)+ϵ−X0. X_t=Y_γ-X_0=γ(C-X_0)+ε-X_0. Following the Rectified Flow argument, the population velocity field is given by the conditional expectation (66) v⋆(x,t,c)=[Yγ−X0|Xt=x,C=c].v (x,t,c)=E\! [Y_γ-X_0\, |\,X_t=x,C=c ]. At the population level, with this exact velocity field and exact ODE integration, the induced flow preserves the conditional interpolation marginals: (67) Law(Zt∣C=c)=Law(Xt∣C=c),t∈[0,1].Law(Z_t C=c)=Law(X_t C=c), t∈[0,1]. Thus, RRF inherits the marginal-preserving property of Rectified Flow while introducing an observation-aware residual endpoint. The residual endpoint further yields an exact acceleration point. Since (68) Xt=[1−(1+γ)t]X0+γtC+tϵ,X_t=[1-(1+γ)t]X_0+γ tC+tε, the coefficient of the unknown clean image X0X_0 vanishes at (69) t⋆=11+γ.t = 11+γ. Hence, (70) Xt⋆=γ1+γC+11+γϵ,X_t = γ1+γC+ 11+γε, which depends only on the observed condition C and Gaussian noise. This allows RRF to start sampling from a noisy LQ-related state and integrate only over the shortened interval [0,t⋆][0,t ]. Consequently, the RRF training objective is obtained by substituting the residual path velocity into the standard Rectified Flow objective: (71) ℒRRF(θ)=∫0t⋆[‖vθ(Xt,t,C)−(γ(C−X0)+ϵ−X0)‖22]t.L_RRF(θ)= _0^t E [ \|v_θ(X_t,t,C)- (γ(C-X_0)+ε-X_0 ) \|_2^2 ]dt. In this sense, RRF keeps the linear interpolation and marginal-preserving structure of Rectified Flow, but shifts the endpoint from pure Gaussian noise to a residual-aware stochastic endpoint. This endpoint change is what enables noisy-LQ initialization and accelerated sampling. Appendix H More Visual Results We provide additional visual comparisons to complement the quantitative results. These examples cover real-world benchmarks, synthetic benchmarks, and challenging face restoration cases, showing the behavior of ScaleResfusion under diverse degradation patterns. Overall, ScaleResfusion better preserves input structures while recovering realistic local details, and it avoids the over-smoothed textures, semantic drift, or hallucinated artifacts that can appear in competing restoration methods. Figure 22. More visual comparison on DRealSR with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 23. More visual comparison on RealSR with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 24. More visual comparison on LSDIR-Val with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 25. More visual comparison on LSDIR-Val with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 26. More visual comparison on LSDIR-Val with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 27. More visual comparison on LSDIR-Val with existing diffusion-based restoration methods. The left side shows the results of ScaleResfusion, while the right side compares local crops. Overall, ScaleResfusion better preserves the global structure while recovering more natural details without the over-smoothing or hallucinated patterns observed in competing methods. Figure 28. More visual comparison on DIV2K-Val with existing diffusion-based restoration methods. The left side shows the HQ reference images, while the right side compares local crops. Overall, ScaleResfusion recovers more natural details while remaining faithful to the HQ references, avoiding the over-smoothing or hallucinated patterns observed in competing methods. Figure 29. More visual comparison on DIV2K-Val with existing diffusion-based restoration methods. The left side shows the HQ reference images, while the right side compares local crops. Overall, ScaleResfusion recovers more natural details while remaining faithful to the HQ references, avoiding the over-smoothing or hallucinated patterns observed in competing methods. Figure 30. More visual comparison on WebPhoto-Test (Wang et al., 2021a), an in-the-wild face restoration benchmark without paired ground truth. In this zero-shot setting, ScaleResfusion better handles out-of-distribution degradations and restores more natural facial details than competing methods. Figure 31. More visual comparison on WebPhoto-Test (Wang et al., 2021a), an in-the-wild face restoration benchmark without paired ground truth. In this zero-shot setting, ScaleResfusion better handles out-of-distribution degradations and restores more natural facial details than competing methods. Figure 32. More visual comparison on WebPhoto-Test (Wang et al., 2021a), an in-the-wild face restoration benchmark without paired ground truth. In this zero-shot setting, ScaleResfusion better handles out-of-distribution degradations and restores more natural facial details than competing methods. Figure 33. More visual comparison on WebPhoto-Test (Wang et al., 2021a), an in-the-wild face restoration benchmark without paired ground truth. In this zero-shot setting, ScaleResfusion better handles out-of-distribution degradations and restores more natural facial details than competing methods.