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1. Bibliographic Information

Title: Uncertainty-guided Perturbation for Image Super-Resolution Diffusion Model
Authors: Leheng Zhang, Weiyi You, Kexuan Shi, Shuhang Gu.
- Affiliations: All authors are affiliated with the University of Electronic Science and Technology of China. The corresponding author, Shuhang Gu, is a notable researcher in the field of low-level computer vision.
Journal/Conference: This paper is available as a preprint on arXiv. The link provided ( $arxiv.org/abs/2503.18512$ ) suggests a future publication date, which is likely a placeholder or an error in the link. As of late 2025, it should be considered a very recent work. arXiv is a standard platform for disseminating research in fields like machine learning prior to formal peer review and publication.
Publication Year: The arXiv identifier suggests 2025.
Abstract: The paper proposes a novel approach for diffusion-based image super-resolution (SR) that improves the utilization of low-resolution (LR) image information. The core idea is that different regions of an LR image correspond to different effective "timesteps" in a diffusion process. Flat areas are considered "closer" to the high-resolution (HR) target and require less noise, while complex texture/edge regions are "farther" and need more noise. The authors associate this property with uncertainty, proposing an Uncertainty-guided Noise Weighting (UNW) scheme where pixels with lower estimated uncertainty (flat regions) receive less noise perturbation. This preserves more of the original LR information. The paper also introduces a modified, more efficient network architecture, culminating in the Uncertainty-guided Perturbation Super-Resolution (UPSR) model. The authors claim that UPSR outperforms state-of-the-art methods quantitatively and qualitatively, despite having a smaller model size and lower training costs.
Original Source Link: https://arxiv.org/abs/2503.18512 (Preprint).

2. Executive Summary

Background & Motivation (Why):
- Core Problem: The paper addresses the task of real-world single image super-resolution, where the goal is to restore a high-resolution image from a low-resolution one that has undergone complex, unknown degradations.
- Current State: Diffusion models have shown great promise for SR, often producing more perceptually realistic results than Generative Adversarial Networks (GANs). However, existing diffusion-based SR methods have limitations. Some start from pure Gaussian noise (SR3), which is inefficient and ignores valuable LR information. Others, like ResShift, embed the LR image into the initial noise map, but apply a uniform (isotropic) level of noise across the entire image.
- Identified Gap: The key insight of this paper is that treating all image regions equally is suboptimal. Flat, simple regions in an LR image are already very close to their HR counterparts, while complex, textured regions have lost significant information and are "far" from the target distribution. Applying a high level of noise uniformly can corrupt the already-good flat regions, making the reconstruction task unnecessarily difficult.
- Innovation: The paper introduces an anisotropic (region-specific) noise perturbation strategy. It proposes that the amount of noise added to each pixel should be proportional to the "uncertainty" of that pixel's reconstruction.
Main Contributions / Findings (What):
1. Uncertainty-guided Noise Weighting (UNW): A novel technique that modulates the initial noise level in the diffusion process based on an uncertainty estimate of the LR image. Flat regions (low uncertainty) get less noise, preserving details, while textured regions (high uncertainty) get more noise to facilitate the generation of realistic details.
2. A Practical Uncertainty Estimator: The paper proposes using the residual from a pre-trained, lightweight SR network as a proxy for reconstruction uncertainty. The logic is that the difference between an initial SR guess and the upscaled LR image, $|g(y) - y|$ , closely approximates the true residual, $|x - y|$ .
3. An Efficient Architecture (UPSR): The proposed UPSR model integrates UNW and replaces the computationally heavy VQGAN autoencoder (used in prior works like ResShift) with a simple PixelUnshuffle operation. This significantly reduces model size, training time, and memory footprint without sacrificing performance.
4. State-of-the-Art Performance: Experimental results show that UPSR achieves superior perceptual quality on various synthetic and real-world SR benchmarks compared to existing GAN-based and diffusion-based methods, all while being more computationally efficient.

Foundational Concepts:
- Single Image Super-Resolution (SR): The task of creating a high-resolution (HR) image from a single low-resolution (LR) counterpart.
  - Classical SR: Assumes a simple, known degradation model, like bicubic downsampling.
  - Real-World SR: Deals with complex, unknown degradations, including blur, noise, and compression artifacts, making it a more challenging and practical problem.
- Generative Adversarial Networks (GANs): A class of generative models consisting of a generator that creates fake data and a discriminator that tries to distinguish fake from real data. In SR, GANs like ESRGAN and BSRGAN are used to generate photorealistic textures, excelling in perceptual quality.
- Diffusion Probabilistic Models (DPMs): A powerful class of generative models that learn to reverse a gradual noising process.
  - Forward Process: A fixed process that slowly adds Gaussian noise to an image over a series of timesteps $T$ , eventually turning it into pure noise.
  - Reverse Process: A learned neural network (typically a U-Net) that denoises the image step-by-step, starting from noise and gradually generating a clean image. This process is guided by the score (gradient) of the data distribution.
Previous Works & Technological Evolution:
- The field of SR has moved from traditional methods to deep learning. Early deep learning models focused on improving fidelity metrics like PSNR using CNNs (SRCNN, EDSR).
- GAN-based SR: ESRGAN and its successors like BSRGAN and Real-ESRGAN shifted the focus to perceptual quality, using GANs to synthesize realistic details for real-world degradations.
- Diffusion-based SR:
  - SR3 and SRDiff were early works that adapted diffusion models for SR. They treated SR as a conditional generation task, starting from pure noise and using the LR image as a condition. However, this is inefficient as it reconstructs the entire image from scratch.
  - LDM-SR improved efficiency by performing the diffusion process in a compressed latent space learned by an autoencoder (VQGAN).
  - ResShift made a key improvement by changing the initial state of the diffusion process. Instead of starting from pure noise $\epsilon$ , it starts from the upscaled LR image plus noise: $x_T = y_0 + \epsilon$ . This reframes the task as learning the residual between the LR and HR images, which is an easier problem. ResShift serves as the direct baseline for this paper.
Differentiation:
- ResShift vs. UPSR: While ResShift introduces the crucial idea of residual diffusion, it applies noise isotropically (uniformly). UPSR refines this by applying noise anisotropically (non-uniformly), guided by the estimated uncertainty of each image region.
- Architectural Efficiency: UPSR further improves on ResShift and LDM-SR by replacing the heavy VQGAN module with a lightweight PixelUnshuffle operation, making the model significantly more efficient to train and deploy.

4. Methodology (Core Technology & Implementation)

The core of the paper is the development of an adaptive, content-aware noise injection scheme for diffusion-based SR.

Principles & Motivation: The authors first analyze the relationship between noise level, fidelity, and perceptual quality.

$Figure 2. (a) The distribution of pixel residual $| y - x |$ computed on ImageNet-Test dataset \[44\], omitting values where $| y - x | >$ 0.4 for clarity. The result exhibits a distinct long-tailed ch…$ 该图像是图表，展示了超分模型。(a) 像素残差 $|y-x|$ 呈长尾分布。(b) 保真度 $|f(y)-x|$ 随残差稳定，感知质量 $|\phi(f(y))-\phi(x)|$ 对噪声更敏感，高残差区域需大噪声。图示加权噪声 $w_u(\boldsymbol{y})\sigma_{max}$ 。

As shown in Figure 2, they observe:
1. The pixel-wise residual $|y - x|$ between the upsampled LR image and the HR ground truth follows a long-tailed distribution. Most pixels have a small residual (corresponding to flat areas), while a few have a large residual (edges and textures).
2. Fidelity (reconstruction error) is not very sensitive to the initial noise level ( $\sigma_{max}$ ).
3. Perceptual quality is highly sensitive. For regions with a large residual (high complexity), a larger noise level is needed to generate plausible details and avoid overly smooth results. Conversely, for flat regions, a large noise level is unnecessary and can be harmful.
  
  This motivates the core idea: the noise level should adapt to the local image content.
Uncertainty Estimation: To adapt the noise, a measure of regional complexity or "difficulty" is needed. The authors frame this as uncertainty. Regions with high information loss (edges, textures) are harder to restore and thus have high uncertainty. They propose a simple yet effective method to estimate this:
1. The true residual $|x^i - y^i|$ is a good indicator of uncertainty.
2. At inference time, the true HR image $x^i$ is unknown. So, they use a pre-trained auxiliary SR network $g(\cdot)$ to generate an initial SR estimate $g(y^i)$ .
3. They show that the estimated residual $|g(y^i) - y^i|$ is a good proxy for the true residual.
  
  $Figure 3. A visualization of the actual residual $| { \\boldsymbol x } ^ { i } - { \\boldsymbol y } ^ { i } |$ and the estimated residual $| g ( \\pmb { y } ^ { i } ) - \\pmb { y } ^ { i } |$ .The real r…$ 该图像是图3插图，展示了HR、LR图像及对应的真实残差 $| { \boldsymbol x } ^ { i } - { \boldsymbol y } ^ { i } |$ 和估计残差 $| g ( \pmb { y } ^ { i } ) - \pmb { y } ^ { i } |$ 。真实残差在边缘和纹理区域显示高值，表明不确定性高。SR网络估计的残差与真实残差接近，可有效估计不确定性。
Figure 3 visually confirms that the estimated residual map is structurally similar to the real residual map. The uncertainty estimate is formally defined as: $\psi _ { e s t } ( { \pmb y } ) = \frac { 1 } { 2 } | \pmb { g } ( { \pmb y } ) - { \pmb y } |$ Here, $\pmb{y}$ is the upscaled LR image, and $g(\cdot)$ is the auxiliary SR network.
Uncertainty-guided Noise Weighting (UNW): With the uncertainty estimate, the paper introduces a diagonal weight matrix $w_u(\pmb{y})$ to modulate the noise. The weight for each pixel is a monotonically increasing function of its uncertainty. $w _ { u } ( { \pmb y } ) : = u ( \psi _ { e s t } ( { \pmb y } ) )$ The supplementary material specifies the function $u(\cdot)$ as a piecewise linear function: $u ^ { \prime } ( \psi ) = \left\{ \begin{array} { l l } { \frac { \left( 1 - b _ { u } \right) } { \psi _ { m a x } } \psi + b _ { u } } & { \mathrm { ~ i f ~ } 0 \leq \psi \leq \psi _ { m a x } } \\ { 1 } & { \mathrm { ~ o t h e r w i s e } } \end{array} \right.$
- $\psi$ is the uncertainty estimate for a pixel.
- $b_u$ is an offset (empirically set to 0.4) to ensure a minimum level of noise is always added.
- $\psi_{max}$ is a threshold (empirically 0.05) beyond which the maximum weight of 1.0 is applied.
  
  ![Figure 7. A combined visualization of the distribution of the residual $| y - x |$ (left), and the weighting coefficient $u ( \\psi _ { e s t } ( y ) )$ with respect to the estimated residual $\\left|…](/files/papers/68efcd33a63c142e6efe1dfb/images/7.jpg) *该图像是图7，一个组合可视化图表。它展示了残差$ |y-x|`的分布（橙色柱状图，对应左侧频率轴）和权重系数`u(\psi_{est}(y))`随估计残差`|y-g(y)|`变化的曲线（蓝色折线，对应右侧权重系数轴）。X轴表示残差/估计残差。残差分布高度集中在0附近。权重系数曲线在估计残差处于[0, 0.1]区间时随输入线性增加，并达到1.0后保持不变。据描述，超过80%的数据其估计残差落在[0, 0.1]区间。*
Figure 7 illustrates this function, showing that for most pixels (with low estimated residual), the noise weight scales linearly, while for the few pixels with very high residual, the weight is capped at 1.0.
Modified Diffusion Process and Overall Pipeline: The UNW is integrated into the ResShift diffusion framework. The forward and backward transition distributions are modified to include the weight term`w_u(\pmb{y}0) $: * **Forward Transition:**$ w_u(\pmb{y}0)^2 $. * **Backward Transition:**$ y_0 $估算的不确定性图$ u(\psi{est}(y_0)) $，引导高斯噪声$ \epsilon \sim N(0, \sigma^2I) $的区域权重。模型通过迭代去噪和上采样，最终从$ x_T $生成高分辨率图像$ x_0 $。](/files/papers/68efcd33a63c142e6efe1dfb/images/4.jpg) *该图像是UPSR扩散模型的流程图。它展示了如何利用低分辨率图像$ y_0 $估算的不确定性图$ u(\psi{est}(y_0)) $，引导高斯噪声$ \epsilon \sim N(0, \sigma^2I) $的区域权重。模型通过迭代去噪和上采样，最终从$ x_T $生成高分辨率图像$ x_0 $。* 1. Given an LR input$ y_0 $, an auxiliary SR network$ g(\cdot) $computes an initial SR estimate$ g(y_0) $. 2. The uncertainty map$ \psi_{est}(y_0) $and the noise weight map$ w_u(y_0) $are calculated. 3. The initial state$ x_T $is created by adding the uncertainty-weighted noise to$ y_0 $. 4. The reverse diffusion process is executed by a U-Net denoiser$ f_\theta(\cdot) $, which takes the noisy image$ x_t $, timestep$ t $, and both$ y_0 $and$ g(y_0) $as conditional inputs. 5. The final output is the denoised image$ x_0 $. * **Network Architecture Modification:** The paper replaces the VQGAN encoder/decoder used in `ResShift` for latent space diffusion. Instead, it uses `PixelUnshuffle` to reduce spatial resolution (and increase channel depth) before the U-Net, and a simple nearest-neighbor upsampling followed by a convolution to restore it. This is a much lighter approach that avoids the massive parameter count and computational cost of VQGAN, making `UPSR` more efficient. # 5. Experimental Setup * **Datasets:** * **Training:** `ImageNet` dataset, with$ 256 \times 256 $patches as HR targets. * **Degradation:** LR images ($ 64 \times 64 $) are generated using the degradation pipeline from `Real-ESRGAN`, which simulates real-world artifacts. * **Testing:** * `ImageNet-Test`: A synthetic test set. * `RealSR` & `RealSet65`: Standard real-world SR benchmark datasets. * **Evaluation Metrics:** * **Full-Reference Metrics (Fidelity):** 1. **PSNR (Peak Signal-to-Noise Ratio):** Measures the pixel-wise reconstruction accuracy. Higher is better. * **Conceptual Definition:** It is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects its fidelity. It is expressed in decibels (dB). * **Formula:**$ \mathrm{PSNR} = 10 \cdot \log_{10} \left( \frac{\mathrm{MAX}I^2}{\mathrm{MSE}} \right) $, where$ \mathrm{MSE} = \frac{1}{mn} \sum{i=0}^{m-1} \sum_{j=0}^{n-1} [I(i,j) - K(i,j)]^2 $. * **Symbols:**$ \mathrm{MAX}I $is the maximum pixel value (e.g., 255),$ I $is the ground truth image,$ Kg(y_0)g(\cdot) $. A poor$ g(\cdot) $could lead to suboptimal noise weighting. * **Heuristic Weighting Function:** The piecewise linear function for mapping uncertainty to noise weights is hand-designed and based on empirical settings ($ b_u=0.4, \psi{max}=0.05$). Future work could explore learning this function or finding a more principled formulation.
- Task Specificity: While highly effective for SR, the generalizability of this specific uncertainty estimation method to other image restoration tasks (e.g., deblurring, inpainting) is an open question.
Personal Insights & Critique:
- Elegant and Intuitive Idea: The core concept of linking image complexity to the required noise level in a diffusion model is both powerful and intuitive. It elegantly addresses a key limitation of prior methods that treat all pixels equally.
- Practical Significance: The architectural simplification (replacing VQGAN) is a major practical contribution. High training costs are a significant barrier to the adoption and development of diffusion models, and this work shows that for certain tasks, expensive latent space representations may not be necessary, especially with few sampling steps.
- Future Impact: This work is likely to inspire more research into content-aware or adaptive diffusion processes. The idea of modulating noise or other diffusion parameters based on input characteristics could be extended to other conditional generation tasks, not just in image restoration but also in areas like text-to-image synthesis (e.g., applying more noise to background regions and less to foreground subjects). It represents a step towards making diffusion models not just powerful, but also more intelligent and efficient.