KernelFusion: Zero-Shot Blind Super-Resolution via Patch Diffusion
Authors: Oliver Heinimann
Tal Zimbalist
Assaf Shocher
michal Irani
Venue: ICLR 2026 Poster (2026)
Keywords: Kernel Estimation
Super Resolution
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Traditional super-resolution (SR) methods assume an "ideal'' downscaling SR-kernel (e.g., bicubic downscaling) between the high-resolution (HR) image and the low-resolution (LR) image. Such methods fail once the LR images are generated differently. Current blind-SR methods aim to remove this assumption, but are still fundamentally restricted to rather simplistic downscaling SR-kernels (e.g., anisotropic Gaussian kernels), and fail on more complex (out of distribution) downscaling degradations. However, using the correct SR-kernel is often more important than using a sophisticated SR algorithm. In "KernelFusion'', we introduce a zero-shot diffusion-based method that uses an unrestricted kernel. Our method recovers the unique image-specific SR-kernel directly from the LR input image, while simultaneously recovering its corresponding HR image.  KernelFusion exploits the principle that the correct SR-kernel is the one that  maximizes patch similarity across different scales of the LR image.  We first train an image-specific patch-based diffusion model on the single LR input image, capturing its unique internal patch statistics. We then reconstruct a larger HR image with the same learned patch distribution, while simultaneously recovering the correct downscaling  SR-kernel that maintains this cross-scale relation between the HR and LR images. Empirical results demonstrate that KernelFusion handles complex downscaling degradations where existing Blind-SR methods fail, achieving robust kernel recovery and superior SR quality. By breaking free from predefined kernel assumptions and training distributions, KernelFusion establishes a new paradigm of zero-shot Blind-SR that can handle unrestricted, image-specific kernels previously thought impossible.

Published as a conference paper at ICLR 2026
KERNELFUSION: ZERO-SHOT BLIND SUPER-RESOLUTION VIA PATCH DIFFUSION
Oliver Heinimann"
Tal Zimbalist Assaf Shocher
Michal Irani
Weizmann Institute of Science Technion
foliver wwlive..heinimare maniinmmmannj.mmmm mammmaannn@@eeee @we zmann ac.il
(a) Current SR methods fail when downscaling kernels are complex (non-Gaussian):
Recent SR Methods
Interpolation
Kerne|Fusion
Input
SwiniR
StableSR
Bicubic Interp
Interp with Gr Karnel
Recovered SR-Kemel
Recovered
Image
STOTE BAM
STATE BAM
STATE Bdlk Madtvol
STATE BAM MARKET
STATE BANK Of
MORIET
BNEEET on
23.775
24,865
25.733
(b) Existing Kernel estimation methods cannot recover complex SR-Kernels:
LR Input Image
Ground Truth
KemalGAN- 255R
IKR
MLMC
DKP
KernelFusion
FUN
FUN
The importance of an accurate SR-Kernel. (A) SotA SR-methods fail complex downscaling kernels, performing than interpolation such kernlss. (B) Existing SR-kernel estimation methods cannot handle complex kernels. KernelFusion the only method capable estimating arbitrary SR-kemels.
Figure 1:
ABSTRACT
Traditional super-resolution (SR) methods assume an "ideal" downscaling SR- kernel (e.g., bicubic downscaling) between the high-resolution (HR) image and the low-resolution (LR) image. Such methods fail once the LR images are gen- erated differently. Current blind-SR methods aim remove this assumption, but are still fundamentally restricted to rather simplistic downscaling SR-kernels (e.g., anisotropic Gaussian kernels), and fail on more complex (out of distribu- tion) downscaling degradations. However, using the correct SR- SR-kernel is often more important than using sophisticated SR algorithm. introduce zero-shot diffusion-based method that uses an unrestricted kernel. Our method recovers the unique image-specific SR-kernel directly from the LR input image, while simultancously recovering its corresponding HR image. KernelFu- sion exploits the principle that the correct SR kernel is the one that maximizes patch similarity across different scales of the LR image. We first train image- specific patch-based diffusion model on the single LR input image, capturing its unique internal patch statistics. We then reconstruct larger HR image with the same learned patch distribution, while simultaneously recovering the correct downscaling SR-kernel that maintains this cross-scale relation between the HR and LR images. Empirical results demonstrate that KernelFusion handles complex downscaling degradations where existing Blind-SR methods fail, achieving robust kernel recovery and superior SR quality. By breaking free from predefined kernel assumptions and training distributions, KernelFusion establishes a new paradigu gm of zero-shot Blind-SR that can handle unrestricted, image-specific kernels previ- ously thought impossible. See project's 's webpage for additional information.
"KernelFusion", we
"These authors contributed equally.

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Published as a conference paper at ICLR 2026
INTRODUCTION
Super-resolution (SR) is an inverse problem of recovering a high-resolution (HR) image from its low-resolution (I.R) counterpart, given by:
IR (IHR ks) bar
(1)
where lig is the downscaling kernel (also known as SR kernel) and 4s denotes subsampling by a scale factor s. Traditional SR methods have achieved impressive results Dong et al. (2015); Lim et al. (2017); Kim et al. (2016); Zhang et al. (2018b;c); Saharia et al. (2022); Li et al. (2024) under the assumption that k2 is global, known kernel (e.g. bicubic with antialiasing), but this is rarely the case. The SR-kernel tends to be amage-specific; it is affected not only by sensor optics. but also by camera motion, subtle hand movements, and other factors. Evidently, these methods perform poorly in any scenario other than synthetic data specifically created using the assumed kernel. In fact, it was shown Levin et al. (2009); Efrat et al. (2013), that the accuracy of the SR-kernel is often more critical for obtaining good SR, than the image prior or the choice of SR algorithm used.
Blind-SR methods have emerged to address this limitation. Some approaches aim to explicitly estimate the unknown kernel (e.g., Michaeli & Irani (2013); Bell-Kligler et al. (2019); Xia et al. (2024)), whereas others represent the SR-kernel implicitly Gu et al. (2019); Luo et al. (2023); Huang al. (2020); Kim et al. (2021); Ates et al. (2023), or aim to design networks that are robust to kernel variations (e.g., Liang et al. (2021); Wang et al. (2024b;a); Luo et al. (2022; 2025); Lin et al. (2024)). However, existing Blind-SR methods are fundamentally limited: They can only super-resolve well LR images which were downscaled by simple, low-pass- pass-filter kernels (e.g.. (an) Gaussians), and fail on more complex downscaling kernels, which are outside their training distribution. In fact, for LR images obtained by non- Gan-Gaasiaan downscaling kernels, SOTA Blind-SR methods perform worse than simple interpolation. (see Fig. la and Sec. 3).
In "KemelFusion", , we introduce zero-shot diffusion- based method that makes no assumptions (ex- plicitly or implicitly) about the downscaling kernel, other than the kernel being global. Our method recovers the unique image-specific SR-kemel directly from the LR input image, while simulta- neously recovering its corresponding HR image. KernelFusion exploits the principle (presented by Michaeli & Irani (2013) and used in Bell-Kligler et al. (2019)), that the correct SR-kernel is the one that also maximizes patch similarity across different scales of the LR image. More specifically, first train an image-specific match-based diffusion model on the single LR input image, capturing its unique internal patch statistics. We then reconstruct the larger HR image during the reverse dif- fusion process, enforcing the same patch distribution, while simultaneously estimating downscaling SR-kernel. While existing methods excel at handling Gaussian kernels, empirical results show that KernelFusion succeeds in recovering valid kernels and reconstructions under complex degradations, scenarios where prior Blind-SR methods tend to break down.
The ability of KernelFusion to handle complex downscaling kernels (where all previous SR methods fail), stems from the following critical design choices:
1. Being a zero-shot estimation method which trains internally on the LR input image only, Kernl- Fusion is not bound by any external training distribution, hence can handle any type of downscaling kernel. There no notion of -fuitrrddistittution kernels, which etteraall-trriieed Blind-SR meth- ods suffer from (see Fig. la).
kernlls,,
2. Previous zero-shot SR-kernel methods Michaeli & Irani (2013); Bell-Kligler et al. (2019) esti- mated the kernel only, requiring a separate independent SR algorithm to super-resolve the LR image with their recovered kernel (e.g., using ZSSR Shocher et al. (2018b) or SRMD Zhang et al. (2018a), which can receive user-specified kernel). Such 2-step process suffers from accumulated errors and inconsistencies between the estimated kernel and the estimated HR image. In contrast, Kernel- Fusion simultunewuslly estimates both the SR-kernel and the HR image in consisteni manner.
3. The explicit kernel estimation methods of Bell-Kligler et al. (2019); Xia et al. (2024); Ates et al. (2023); Yang et al. (2024b) seem to recover well only specific types of kernels (Gaussians and motion lines). We suspect that this limitation stems from the implicit-ber bias of the CNN and MLP architectures, which tend to produce smooth outputs (as also observed in Tancik et al. (2020)). In contrast, the kernel-estimation component in KemeeFusiio employs an Implicit Neural Representa- tion (INR) architecture, which recovers complex non-smooth downscaling SR- Be-kernels (see Fig. 1).
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Phase Patch Diffusion (PD) Training
Phase 2: Blind Super Resolution
Estimated HR
Input Image
HR Guesa
XY coords
Unet
Noise
PD
Unet
legresentitonng
Implici
MSE Loss
Noise
D Duy
MSE Loss
Estimated
Crop
LR Input Image
Estimated LR Image
Figure 2: Method Overview. Our approach consists of 2 stages: Phase We train a diffusion model (PD) to learn the patch distribution of single image. Phase 2: We perform blind SR and kemell estimation simultaneously. In particular, we use the trained PD to shift the HR guess toward the patch distribution of the LR input. A refinement U-Net and implicit kernel representation model trained jointly under consistency loss, ensuring that convolving the estimated HR image with the learned kernel reproduces the original image.
Our aim is not to deliver production-ready Blind-SR system, but to establish feasibility of un- restricted kernel estimation from a single LR image while simultaneously recovering the HR im- age. By breaking free from predefined kernel assumptions and training distributions, KernelFu- sion pushes Blind-SR into a new, assumption tareettoooeeeeeee free paradigm handling out-of-diistibution data and downscaling kernels which were previously out of reach.
KernelFusion is the first deep Blind-SR method able to recover arbitrary downscaling kernels.
Since KernelFusion trains on LR input image, there no notion of "outtof-distriiutiion" data. It is trained to adapt to the image-specific data and downscaling kernel.
KernelFusion provides state-of-the-art SR results on challenging out-of-distributton data, where leading SR methods fail (while being competitive within distribution).
RELATED WORK
We first deseribe three main types of Blind-SR Liu et al. (2022). We then review diffusion models and their use for inverse problems, which is related to our method.
Blind-SR trained on synthetic degradations: These methods train on LR images generated by synthetic degradations from predefined distribution of degradations. When applied to data close to that distribution they achieve visually pleasing results. These include SwinIR Liang et al. (2021), Real-ESRGAN Wang et al. (2021) and many more Conde et al. (2022); Zhang et al. (2021); Jo et al. (2021); Luo et al. (2022); Lin et al. (2024); Sun et al. (2024); Wu et al. (2024b); Wei et al. (2020); Yang et al. (2024a); Zhang al. (2024); Wu et al. (2024a); Chen et al. (2025). Such methods are restricted by their training distribution, thus fail on LR images generated by nut-of-distribution downscaling kernels (e.g., non-Gaussian kernels).
Blind-SR with latent kernel representation: Other methods represent degradations by a latent features vector. These methods perform SR and refinement of the degradation features, often based on alternating SR and latent kernel estimation. This was first shown by IKC Gu et al. (2019), later improved by unfolding this alternation with DAN Huang et al. (2020); Luo al. (2023) and others Luo et al. (2022); Kim et al. (2021); Zhang et al. (2020); Sohl-Dickstein et al. (2015); Mehta et al. (2025). The kernel representation data-driven, hence also based on the synthetic degradations used at training. These methods too, fail on images downscaled by kernels out of their training distribution.
Blind SR-Kernel Estimation: Acknowledging the importance of an accurate SR-kernel, some approaches aim to explicitly estimate the unknown SR-kernel directly from the LR image (e.g., Michaeli & Irani (2013); Bell-Kligler et al. (2019); Xia et al. (2024); Ates et al. (2023); Yang et al. (2024b); Tao et al. (2021)). Notably, Michaeli Irani (2013) was the first to observe that the optimal SR-kemnel is the that maximizes the similarity of small patches across different scales of the LR image, and accordingly used cross-scale patch nearest- neighbors to estimate the SR- kernel. KernelGAN Bell-Kligler al. (2019) further used this principle within deep learning, showing that
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GT Image
GT
Bicubic
SinSR
SwinlR
StableSR
DIFFBIR
DCLS
ReaiDAN
Ours
Figure 3: Blind-SR comparison on the DIV2KFK dataset (4x SR). Each row relates to a different LR image from DIV2KFK, while each column shows the output of different method. Notably, our method reduces doubling artifacts in structured patterns (e.g., aerial road scene, 4th row). demonstrating its effectiveness in restoring fine details and mitigating motion effects.
the SR-kernel can be estimated by training an image-specific GAN on the LR image. However, the zero-shot methods of Michaeli & Irani (2013); Kligler et al. (2019) are pure kernel estimation methods. They do not perform any SR, hence require a separate followup algorithm to perform the SR step on the LR image (e.g., using ZSSR Shocher et al. (2018h) or SRMD Zhang et al. (2018a)), which can receive a user-specified kernel as an input. This restricts their applicability. Moreover, the explicit kernel estimation methods of Bell-Kligler et al. (2019); Xia et al. (2024); Ates et al. (2023); Yang et al. (2024b) can only recover well specific types of kernels (Gaussians and motion lines see examples in Fig. 1).
Diffusion Models and Inverse Problems: Diffusion probabilistic models Sohl-Dickstein et al. (2015); Ho et al. (2020) have become a powerful tool for modeling complex image distributions. More recently, under the Deep Internal Learning regime Shocher et al. (2018b); Gandelsman et al. (2019); Ulyanov et al. (2018); Shocher et al. (2018a); Shaham et al. (2019); Granot et al. (2022) liffusion-based approaches have been adapted for the single-image setting Nikankin al. (2023); Wang et al. (2022); Kleiner et al. (2023). Additionally, diffusson models have shown promise in solving inverse problems such as deblurring and super-resolution Kawar et al. (2022); Chung et al. (2022). Recent works further enhance these approaches by incorporating data-consistency con- straints via null-space projections Wang al. (2023) or by adding projeproee steps Hui et al. (2024). Plug-and-play (PnP) adaptions to diffusion or flow matching, such as Zhu et al. (2023); Martin et al. (2024), use the model as denoiser in an iterative reconstruction algorithm. However, these methods do not cover the case of blind SR. Additional work on patch-based diffusion mod- els Altckrüger et al. (2023); Hu et al. (2024a;b) further exploits local image statistics for improved detail recovery. Due to their stochastic nature, diffusion models struggle to adhere to measurement constraints. Moreover, they may exhibit a distribution mismatch between the training data and the observed measurements, necessitating careful adaptation Hu et al. (2024b). A related line of work leverages diffusion priors for kernel estimation in inverse problems, most notably BlindDPS Chung al. (2023), which tackles blind deblurring and imaging through turbulence. While conceptually related to KernelFusion, BlindDPS operates in a different regime, relying on pre-trained diffusion models over images and kernels trained on large synthetic blur datasets, whereas KernelFusion is entirely zero-shot.
3 THE IMPORTANCE OF AN ACCURATE SR-KERNEL
The accuracy of the SR-kernel is critical for achieving high-fidelity HR image reconstruction, often playing a more crucial role than the image prior or SR method itself Efrat et al. (2013); Levin et al. (2009). The SR process fundamentally relies on inverting the degradation introduced by downsam-
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KernelFusion (Ours)
KernelFusion (Ours)
KemeeGAN
KernelGAN
IKR
IKR
MLMC
MLMC
DKP
DKP
Figure 4: Comparison of estimated kernels from different Blind-SR methods. The top row represents the ground-truth (GT) degradation kernels, while each subsequent corresponds to the estimated kernels from different SR methods, including our approach, KemnelGAN, IKR, MLMC, and DKP. Our method demonstrates superior flcxibility in recovering complex, non-Gaussian degradations, accurately capturing kernel structures across a diverse range of degradations.
pling, which is dictated by the underlying kernel. If the kernel is inaccurate or out of distribution, even advanced SR models risk producing artifacts and unrealistic results.
This property is shown in Fig. I: Two leading algorithms (SwinIR & StableSR), both trained with blind SR degradations, fail to accurately upscale LR images which were downscaled by non- Gaussian kernels. In contrast, simple interpolation leads to remarkably better visual results. We further confirm this observation quantitatively on datasets with hundreds of LR images down- scaled by a variety of non-gaussian kernels ("Blind144" & "DIV2KFK" - see Sec. 5. These results are summarized
Table 2, and a sample is displayed here (in Table 1), showing that even SotA Blind-SR methods (DPSR Zhang et al. (2019), DCLS Luo et al. (2022)) perform worse than sim- ple bicubic interpolation on non-gaussian kernels (which are outside their training distribution). Moreover, applying more sophisticated interpolation with the ground-truth (GT) kernel provides an additional large improvement (by + +dBB over SotA Blind-SR methods on such kernels.
METHOD: "KERNELFUSION" FOR BLIND-SR
Table 1: SotA Blind-SR meth- ods perform worse than interpo- lation on LR images downscaled by non-Gaussian kernels.
Our method builds on the principle that the correct SR kernel is the one that best preserves the image's s patch distribution across scales. In a first step, patch-based diffusion model trained on the LR input image, learning its patch distribution. In a second step, we perform super resolution by iteratively improving our HR guess and estimating the SR-kernel during the reverse diffusion process. Fig. 2 provides an overview over our approach.
Method
Blind144 DIV2KFK
Bicubic
24.865
24.101
GT kemel
25.733
25.057
DPSR
24.824
23.997
Phase 1: Training Patch-Diffusion (PD): Our Patch-Diffusion (PD) model aims to learn the patch distribution of the LR input image Inn- As diffusion models excellent distribution learn- ers, we base our model on the standard denoising probabilistic diffusion model (DDPM) Ho et al. (2020), predicting a velocity (inspired by Salimans & Ho (2022)). We motivate the parametriza- tion by the increased stability i.c. at few sampling steps. We train to denoise solely the single LR input image noised with various noise magnitudes. according to a standard DDPM schedule. More specifically, the input is a diffused IL to random time step t E [1,7]] while the target is the velocity (from which one can easily derive the clean original input image using closed form):
DCLS-SR
24.808
23.886
V argming PD (Ix) =ell; where =,= āge, -==vaje-11- - āyAo, V are the parameters of our PD model, e a standard normal white noise, zo = IL the LR input, a the standard DDPM coefficient, and d = I ag.
"Interpolation with a kernel is obtained by hackprojection Trani & Peleg (1991) with the estimated Pseudo- Inverse Moore (1920); Penrose (1955) of the kemee.
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Learning the patch distribution of single image requires some adjustments: We took inspiration from Nikankin et al. (2023) using pure CNN without any global layers (such as attention). However, since our method is based on much smaller patches, the receptive field needs to be restricted even further. Thus we exchange the backbone with a simple convolutional network with no strides, induc- ing a theoretical receptive field of 15x 15 pixels (and practically much smaller). This allows training PD on random x4 image crops (see Phase in Fig. 2). Note the difference between the larger 64 x64 image "crops", and the smaller "patches" whose distribution is being learned (and whose size is determined by the small PD receptive field). Each random 64x 64 image crop serves as batch of thousands of small image patches. Further design choices, hyperparameters, and implementation details are found in Implementation Details.
Phase 2: Reverse Diffusion at High Resolution: Once PD trained, has learned the patch distribution of the LR input image. Next, we perform simultaneous SR and kernel estimation, based on the reversed sampling process of PID 1 Thiis constrains the produced HR image to have the same patch distribution as LR (which it should have Michaeli & Irani (2013)). This combined approach has a major benefit: A better HR prediction de leads to an improved kernel prediction, and vice versa. The right part of Fig. 2 (labeled as Fig. 2R below) summarizes the main components used in the reversed sampling process while Algorithm in the appendix, provides pseudo-code codue of the approach, which is further detailed below. Our method takes as initial input a bicubically upscaled version of the LR image IR (top left Fig. 2R). This bicubic guess is noised by Tud steps using the diffusion noise schedule ("Noise" in Fig. 2R). Subsequently, we would like optimize to each timestep f, such that the downscaled version 2o ta (using the kernel estimated by the INR, Fig. 2R on the right) is consistent with the input image In (bottom row of Fig. 2R). Instead of directly optimizing Lo. we chose to implicitly optimize to via U-Net (see right "UNet" in Fig. 2R). The U-Net (inspired by DIP Ulyanov et al. (2018)) imposes a global image prior on the output. The PD step used to predict do alone does not inherently preserve global structure, especially at high 4, due to the 15x 15 local receptive field of PD (see Appendix D further details). We solve this problem by applying the (same) U-Net twice: First, we apply the U-Net to Do from the previous timestep t + 1 and reconstruct the required ot from it. Second, we apply the U-Net after denoising d using patch-diffusion model PD to the predicted zo timestep t. We refer to Appendix C.2 for more details and intuition. Optimizing the U-Net using our LR consistency loss is hence key to maintain global structure. This setup enables joint training of both the U-Net and the kernel estimation network (see Kernel Estimation using INR) with a single loss. Since both networks are trained from scratch, we apply Riter gradient steps at each timestep f. The networks are iteratively refined at every f, leveraging their gradual improvements to enhance the prediction of in.
Kernel Estimation using INR: Estimating a SR-kernel means solving for k2 in Eq. (1). Instead of directly solving for k,, we chose to represent the kernel via an Implicit Neural Representation (INR) network, which allows us to represent the kernel continuously Shocher et al. (2020), while control- ling its level of regularization. Specifically, we took inspiration by the SIREN architecture Sitzmann et al. (2020) which is known for its ability to also represent high frequency functions. Specifically, the sinusoidal activations enable the network to capture fine-grained structures without introducing over-smoothing, which is critical for accurately estimating complex downscaling kernels kgg See A.4 for more details.
Consistency Loss: In Phase 2, our method relics on a MSE consistency loss (see Eq. (2) to enforce a pixel-wise alignment between the input LR image I IL and the estimated LR image (Øo * R.) 4a- This prevents predicting hallucinated structures not supported by the ILR.
Loons = MSE [I.R: (2o * R..) 4.)
(2)
Implementation Details: To ensure small receptive field of PD, we exchanged the global- receptive-field U-net of the original DDPM architecture with a small, fully convolutional neural net. We one block consisting of two 3x3 convolutions, followed by five blocks 3x3 1x1 convolutions. This results in theoretical receptive field of 15x 15 pixels. The diffusion model is trained with 10-1000 time steps. For more details see appendix A.
Note that during Phase 2, the PD network is frozen with gradients allowed to propagate through it. We indicate this by lock symbol in Fig. 2

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Table 2: Quantitative results on 4x SR across Blind-SR datasets. PSNR/SSIM for a representative set of methods; the two best results per dataset are shown in bold and underline. On the 2 non-Gaussian datasets (DIV2KFK, Blind144), KemnelFusion is able to recover consistent kernels and reconstructions where many prior methods struggle, while bicubic interpolation serves as a surprisingly strong referenee. On the Gaussian DIV2KRK dataset, performance remains comparable to methods explicitly trained for such kernlss. *Comment: The reported PSNRs are after excluding image boundary of 5%, due to boundary effects.
B4i
DIV2KRK
DIV2KFK PSNR SSIM
Method
PSNR SSIM
PSNR SSIM
Bicubic
24.865
0.637
25.075
0.671
24.101
0.639
SinSR Wang et al. (2024b)
23.587
0.582
25.360
0.680
22.887
0.585
StableSR Wang et (2024a)
23.775
0.625
25.262
0.709
23.077
0,630
OSEDiff Wu el. (2024a)
22.841
0.585
23.867
0.658
22.359
0.602
SwinlR Liang et al. (2021)
23.773
0.616
25.139
0.699
23.070
0.620
DPSR Zhang et al. (2019)
24.824
0.637
25.317
0.682
23.977
0.637
IKR Ates et al. (2023)
24.113
0.630
23.906
0.667
23.352
0.627
RealDAN Luo al. (2023)
24.624
0.638
26.870
0.745
23.941
0.644
ReaIDAN gan Luo al. (2023)
23.998
0.619
26.057
0.730
23.439
0.628
RealDAN spec. Luo et al. (2023)
27.821
0.775
DCLS-SR Luo et al. (2022)
24.808
0.633
27.150
0.748
23,886
0.634
DifßBI Lin et al. (2024)
24.259
0.599
25,431
0.668
23,546
0.606
DRAT Chen ct al. (2025)
24.747
0.631
27.953
0.779
23.824
0.631
DKP Yang et al. (2024b)
23.431
0.612
23.127
0.629
22,531
0.603
MLMC Xia et al. (2024)
23,430
0.612
23.122
0.629
22.535
0.604
KemnIGAAN+2SSR Shocher et al. (2018b)
24.529
0.633
25.895
0.703
23.617
0.629
Real-ESRGAN Wang ct al. (2021)
23.646
0.610
24.323
0.678
23.003
0.617
KernelFasion (ours)
27.191
0.719
26.761
0.715
26.426
0.720
GT
KO
K1
K2
K3
K4
K5
K6
K7
KB
K9
K10
K11
Kemels
Inputs
L
C
/
Figure 5: Kernel estimation results on Blind144. The top row displays the 12 ground-truth (GT) degradation kernels, including real-world motion blur kernels from Levin et al. (2009), anisotropic Gaussian kernel, and three synthetic non-natural kernels (L-shape, empty square, and filled square). The subsequent rows show method's estimated kernels for each the 12 kernels applied to 3 sample images the DIV2K validation set. Our approach successfully captures a diverse range of degradations. including complex structured kernels, demonstrating its robustness and adaptability in blind SR kernel estimation.
5
RESULTS
Our evaluation targets unrestricted kernels through (i) complex non-Gausee Gaussian kernels, and (ii) case studies highlighting failure modes of prior methods. Further, we evaluate on a Gaussian bascline.
DIV2KRK Bell-Kligler et al. (2019): LR images were obtained by downscaling each of the 100 im- ages in the DIV2K validation set Agustsson & Timofte (2017), with different random anisotropic Gaussian kernel of varying sizes and orientations.
Inspired by DIV2KRK, we created a new dataset based on the 8 real-life downscaling kernels measured by Levin Levin et al. (2009), which were induced by small camera jitter during the shutter exposure time. We call this dataset DIV2KFK HiV2K--Facy-Kerneee
DIV2KFK:
In order to have reasonable blur levels for 4x SR, we resize the original kernels to size 24x24. Each image of the DIV2K validation set is convolved with randomly selected kernel and sampled by scale of 4.

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Input Image
Ground Truth
KomolGAN 258R
IKR
MLMC
DKP
KernelFusion
Figure 6: Examples explicit SR-kernel estimation and SR under extreme downscaling (Blind144).
Two factors affect the Blind-SR challenge: the image and the downscaling kernel. To further analyze and better understand SR results, we created the controlled Blind144 dataset. It is organized as a 12x 12 matrix comprising 12 images and 12 kernels. This setup allows us examine the results of single kernel across various images, as well as the outcomes of a single image across different kernels, thereby clarifying whether specific effects and behaviors stem from the image or the kernel. The images used are the first 12 images from DIV2K. For the selection of kernels we used the 8 empirical kernels as in DIV2KFK, and in addition extreme stress-testing kernels and one anisotropic Gaussian. The purpose of the Gaussian kernel is to compare quality of results on the same image for in in-distribution vs.
Blind144:
kernels. The 3 extreme kernels contain an "L" shaped kernel, full square with sharp edges, and an empty square. These allow stress-testing of kernel extraction. The full set of kernels shown in the top row Fig.
Empirical Evaluation of SR: Since our goal is to assess accurate reconstruction with respect to ground truth, we use alignment-sensitive metrics such as peak signal-to-noiss ratio (PSNR) and structural similarity index measurement (SSIM) Wang et al. (2004). Perceptual metrics, while ful for visual quality, are less suited for measuring pixel-level fidelity due to alignment insensitivity. We orient our evaluation on the procedure of Kim al. (2016): The evaluation is executed on the luminance channel (YCBCR space). Table 2 compares KernelFusion with representative SotA competitors. Our method able recover accurate kernels and reconstructions on challenging non- Gaussian datasets (DIV2KFK and Blind144), where prior blind-SR methods fail. On the Gaussian DIV2KRK dataset, where existing approaches are specifically tailored to, our results remain com- parable. It is worth noting that simple bicubic upscaling surpasses all SotA methods in PSNR on DIV2KFK & Blind144, indicating that these methods completely fail adapting to out-of-distribution downscaling.
Fig. showcases SR results on DIV2KFK dataset, comparing our method against SotA ap- proaches. Our method demonstrates superior reconstruction quality, particularly in challenging gions such as text, structured patterns, and natural textures. Notably, in Fig. 1, row 1, which contains the State Bank of Mysore sign, most competing methods struggle to recover clear and legible text, often introducing excessive blurring or ghosting artifacts, whereas our method produces sharper, more readable characters. similar trend is observed in the acrial road scene (Fig. row 4), where other methods introduce noticeable doubling artifacts (misaligned white car), which are significantly reduced in our results. Furthermore, our approach maintains balance between sharpness and nat- ural texture preservation in human faces and complex textures, avoiding the over-sharpening and aliasing effects present in some models (e.g., RealDAN, DIFFBIR). These results demonstrate the robustness of our approach in handling diverse realistic degradations as in the DIV2KFK dataset.
Kernel Evaluation: assess the effectiveness of different blind-SR methods in kernel estimation, we visualize the predicted SR-kernels in Fig. 4. The top row represents the ground-truth (GT) ker- nels, while subsequent rows correspond to the estimated kernels from various blind-SR methods that explicitly estimate the SR-kernel (including ours). KernelGAN demonstrates a strong bias to- ward Gaussian-like kernels, failing to accurately capture non- non-Gaussian degradations. IKR Ates et al. (2023), which was trained with mixture of random Gaussian and motion blur kernels, exhibits im- proved performance on motion kernels but struggles to generalize beyond its training distribution, often producing elongated blur patterns. Both ML Xia et al. (2024) and DKP Yang al. (2024b)
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Bicublc
SwiniR
Ours
Keree
MAXIFY
OTH
OM
IRPOSES
3POIES
CEPOLES
DIPCKITS
CIVONSS
OPPORES
CPPOSES
OPPORES
Figure 7: SRx4 diverse real-world images. Each real input image taken from different source. Top-to-Bottom: (i) Image from Lai et (2016), (ii) photo captured with DSLR camera without optical stabilization. (iii) Image from Levin ct al. (2009), (iv) An old historical photo downloaded from the internet. Zoomed-in regions (highlighted in red) show that our method better recovers fine structures, text, and textures compared to SotA Blind SR methods. For example, method clearly recovers the word "OPPOSES" in the old historical photo (bottom), which remains unreadable most competing methads.
leverage meta-learning and Markov Chain Monte Carlo (MCMC) simulations to infer kernel priors without explicit assumptions. As result, they are more flexible capturing diverse degradation patterns. However, despite their adaptive nature, their estimated kernels still exhibit noticeable de- viations from the GT, particularly in the case of extreme degradations. Unlike prior methods, our approach does impose any priors on the kernel shape, allowing it accurately recover chal- lenging degradations. Fig. presents our estimated kernels across samples from the Blind As observed, our approach is capable of recovering diverse range of kernel structures, demonstrating the flexibility of our kernel estimation process. The entire collection of 144 kernels recovered by KernelFusion from the Blind144 dataset can be found in the appendix, Fig. 10. Fig. 6 shows some more SR and kernel extraction comparison for extreme kernels.
Ablations: We ablate the reverse diffusion process described in Phase 2 (see Fig. 2) to identify the individual component contributions (see Table 3): (i) DIP: The UNet gets pure noise as input and is optimized with the consis- tency loss on the downscaled prediction Eq. 2, together with the INR. This corresponds to DIP Ulyanov et al. (2018). We observe that the UNet alone can already account for a certain adjustment of the patch distribution, while making use of the powerful INR. (ii) UNet only: Here, the UNET and the INR are optimized within the full reverse diffusion framework, starting from a partially noised image. At each t, the UNet and INR are optimized for 20 iterations. The DDPM noise scheduler handles the noise between the t's. We observe that this setup already gives a powerful boost in PSNR. (iii) PD + UNET: PD is added to the pipeline of (ii) acting the small receptive field, the network does not know global structure, effectively destroying it at large t's. The UNet compensates the loss of structure induced by PD. (iv) Kernelfusion: Applying the (same) UNet twice, as described in Sec. 4, leads to the best results. The UNet now gets the structural information from the previous making the the optimization easier, while exploiting the patch-die siich-dittribttion adjusted information.
Table 3: Ablations of reverse diffusion
Method
Blind144 PSNR
23.663
UNet only
25.804
PD + UNet
25.481
KernelFusion 27.191
denoiser, predicting in at time f. Due to
To evaluate the performance of our method under realistic degradation con- ditions, we utilize a variety of real-world images from various different sources: (i) The publicly available real-world benchmark of Lai et al. (2016), which consists of naturally degraded images captured in uncontrolled settings from different cameras. (ii) Historic old photos downloaded from the internet. (iii) Real blurry photos from Levin et al. (2009). (iv) Additionally, we captured real images using high-quality DSLR camera where the optical stabilization
Real-World Images:
disabled on purpose. This setup introduces realistic degradations such as mild motion blur and hand tremor common issues in everyday photography. The above collection of diverse real-world photos from different independent sources, taken under completely different settings, makes ideal for testing blind-SR methods in practical scenarios. Fig. 7 shows visual comparisons of 4x SR of our method and the

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leading of-te----teerrtttt Blind-SR baselines. Being real images, there is GT to compare against. Our method reconstructs more accurate details, legible text, well-defined edges, and fine textures that heavily blurred distorted in the competing Blind-SR methods. The complex, non Gaussian kernels estimated by our method, highlight the importance of assumption blind SR. More ex- amples are found in the appendix.
Limitations: While KernelFusion can super-resolve LR images obtained under severe downscaling degradations (previously considered impossible), suffers from several limitations: (i) Operating within the standard SR formulation (Eq. 1), the very quest to estimate the downscaling kernel al- ready implies that unique, globally uniform kernel exists; hence KernelFusion cannot yet handle spatially varying blur. (ii) Our method relies solely on the internal statistics of single natural image (the LR image), without leveraging pre-trained large-scale diffusion models. Although this "assumption-frre " design is central to our ability to tackle previously intractable downscaling degra- dations (has no "out-of- di-tstrbbbution data), it does not exploit rich external information which could further enhance its reconstruction quality. (iii) Runtime: Moreover, Patch-Diffusion (PD) has to be trained from scratch on each new LR image, currently taking 20 mins per image (on single L40S GPU). The subsequent upscaling process depends input image size and the scale factor applied. Exploring ways to integrate external learned priors with our internal PD model may significantly speed up KernelFusion. This represents exciting future research direction.
CONCLUSION
"KernelFusion" recovers the unique image-specific SR-kernel directly from the LR input image, while simultaneously recovering its corresponding HR image in a consistent manner. It can handle complex downscaling degradations, where existing SotA Blind-SR methods struggle. Being zero- shot estimation method which trains internally on the LR input image only, KemelFusion is not bound by any external training distribution, hence can handle any type of downscaling kernel. has no notion of fout-of-distribute By breaking free from predefined kernel assumptions, Kerneluusion pushes Blind-SR into new, unrestricted kernel paradigm handling downscaling degradations previously thought impossible.
data which externally-traiie trained Blind-SR methods suffer from.
7
ACKNOWLEDGMENT
This project was funded in part by the European Union (ERC grant agreement No 101 142115). A.S. is Chaya Fellow, supported by the Chaya Career Advancement Chair.
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Appendix
A FURTHER TECHNICAL DETAILS
A.1 ALGORITHM
Algorithm Reverse Diffusion Process in KernelFusion
1: Input:
2: Pretrained velocity model: pD
3: Number of noise/denoise timesteps: Tnd
4: Noise schedule: {B,]== with Ot 3g
5:
Initial guess: TD, = LR Tbic,s
6: Networks: U-Net Rg. SIREN INRS with grid
7: Center of mass function: COM
8: Number of optimization steps per I: Rater
9: Learning rate: 7
10: Output: Generated sample zo
11: for = Tnd to 1 do
12:
{~ [~N(0,,)
+ Sample noise
13:
for = Nater do
14:
h6 < (g)
Get kernel + Optimize zo
15:
80 - Ro(f0,,41)
16:
80.1+1 4.= (00,1+1.0 * ko) to
+ Downscale step
17:
81,8 - |1++1 (60,1+11 I(+1) + oc+ic
18:
0g + (D,,(fr,H,))
Denoising step
19:
f0.00 yor $2.00
v1 - -0. 60
20:
f0.1. + Ro
+ Optimize xo
21:
6o, 1 (0o,1,0 kp) to
Downscale step
22:
L = ILR Do.t
ts 113
||LR 20.411 to 11 COM(Ns)
23:
A + (L)
Step for U-Net Step for INR
24:
(C)
25:
end for
26:
Ne 31 T-a; $0.0.0 + (1 -0(
yas I-tas f2.
(~ (~,
+ Sample noise
28:
It-1 Me +
+ Add stochasticity, do 0
29:
end for
30:
return 20
A.2 PATCH- DIFFU-DIFUSSON
The backbone model is a convolutional network, that inputs an image tensor ir and timestep t. We have total of 6 blocks, each block conditioned on t. We use block of two 3 x 3 filters, followed by five blocks of 3 x x filters. We use 128 filters for the hidden layers.
Architecture
Training Details The patch diffusion model is trained using random crops of size 64 pixels. The model is trained for 600'000 steps, using Adam as optimizer, with a learning rate of Ir = 1 x 10-4 and cosine annealing. Network weights are initiated using the default configurations of Pytorch.
A.3 U-NET
The refinement UNET consists of 5 blocks, with 32 filters on the input level and 512 filters on the bottom level. Each block consists of convolutional layers with a 3x3 kernel, ReLU activations and batch norm. The final layer uses a tanh activation function to ensure that the predicted To output is the expected- -1 to I range. The levels are down respectively upsampled by scale factor of 2.
Architecture
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Training Details The U-NET is trained at each time step during the reverse diffusion process. We use Adam optimizer, a learning rate Ir = x 10 We apply cosine annealing, reducing the learning rate at each to final Ir reverse diffusion process and then finetuned along the different timesteps t. With the exception of the initial sstrrt where we apply Ritter 100 iterations, the model is then finetune for Biter 20 iterations during each t. Network weights are initiated using the default configurations of Pytorch.
10 The U-NET is initialized at the first start of the
A.4 IMPLICIT NEURAL REPRESENTATION FOR KERNEL ESTIMATION
Architecture As described in Sec. Kernel Estimation, we took inspiration from SIREN Sitzmann al. (2020) for our implicit neural representation. The network consists of fully connected layers, with 256 nodes each. In contrast to the original paper, reduced from 30 to 5 and apply it across all layers. Our last layer has an activation function which we call leaky sigmoid, a sigmoid function also allowing for slight negative values: Oleaky (2) (1 + 10- (Ir) 10-1 1 The kernel is
normalized such that its sum equals to 1. Additionally, as shown in Algorithm 1, a center of mass loss is introduced, encouraging the resulting kernel to be mass centered.
Training Details As train our INR along with the U-NET, we use the same training setup as described in Sec. A.3.
B ADDITIONAL VISUAL EXAMPLES
B. ADDITIONAL KERNEL EVALUATION RESULTS
Fig. 8 shows the results of the estimated kernels for 4 additional images providing additional idence of the effectiveness of KernelFusion compared to current competitors. Fig. 10 provides a complete overview over all estimated kernels of the Blind144 dataset.
B.2 ADDITIONAL REAL LIFE EXAMPLES
Fig. 11 to 18 show additional visual comparisons of real-world images, taken from variety of different sources (the source of each real LR image is mentioned in each example). Our recovered SR-Kernel is also provided for each image. Since these real images, there are NO ground-truth HR images nor ground-truth kernels.
applied on a sample of diverse
C ADDITIONAL ABLATIONS
C.1 KERNEL NETWORK
As described in Sec. 4, KernelFusion leverages an Implicit Neural Representation (INR), specificall SIREN Sitzmann al. (2020) architecture. Alternative architectural choices possible. In the following, two alternative choices are discussed: Directly optimizing the kernel and using a linear CNN e.g. used in KernelGAN Bell-Kligler et al. (2019).
Direct Kernel Optimization: Each entry of the 24 24 kernel grid treated as an individual parameter that is directly optimized. Note that this means that no additional network is applied. Additionally, the optimized kernel positivity (e.g. using ReLU Agarap (2018) activation function) and normalization such that its sum equals to is applied.
Linear CNN: KernelGAN Bell-Kligler et al. (2019) leveraged a deep linear CNN for kernel es- timation. This network consists solely of convolutional layers without any additional activations functions. The network is used to downscale the image and implicitly captures the kernel such. can be explicitly extracted by convolving all layers sequentially (see Bell-Kligler et al. (2019) for more details). Our network consists of 6 convolutional layers with kernll sizes, [7, 7, 5, 3, 1, 4], channels [1, 32, 32, 32, 32, 32, 1] and strides [1, 1, 1, 1, 4]. Not that the last stride entry indicates the scale factor of 4 used in our experimental setup.
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KernelFusion (Ours)
KerneiFusion (Ours)
KerneiGAN
KemeiGAN
IKR
IKR
MLMC
MLMC
DKP
DKP
KernelFusion (Ours)
KernelFusion (Ours)
/
Figure 8: Comparison estimated kernels from different Blind-SR methods. The top row represents ground-truth (GT) degradation kernels, while each subsequent row corresoonds to the estimated kernels from different SR methods. including our approach, KerneIGAN, IKR, MLMC, and DKP. Our method demonstrates superior flexibility in recovering complex, non-Gaussian degradations, accurately capturing kernel structures across a diverse range of degradations.
Table Kernel Network ablations on KO, K1, K2 Blind144
Method
KernelFusion PSNR1
DIP PSNR
Direct Sigmoid
16.366
15.529
Direct Relu
26.541
24.266
Linear CNN
23.494
23.098
INR
26.995
23.638
Experimental Setup: shown in Table 4, we compare four different architectural choices for the kernel estimation: direct kernel optimization (one with a Sigmoid and one with ReLU activation function), KernelGAN like linear CNN, and the SIREN INR applied in KernelFusion. To better show the power our diffusion setup, we additionally evaluated the architectures in a DIP setup (as used in the ablations in Sec. 5).
Results: Table shows the resulting SR PSNRs on the synthetic kernels kgp k1, and k2 of Blind 44 (see Fig. 19 and Fig. 20 for reference). KernelFusion with the INR shows superior results over the alternatives. Nevertheless, the direct optimization using a ReLU activation shows suprisingly good results. However, when comparing the reconstructed kernels (see Fig. 19 and Fig. 20) it becomes clear that the direct optimization leads to noisy, non-consistent kernels. Using an INR, much more accurate kernels can be recovered.
C.2 APPLYING THE U-NET TWICE
As discussed in Sec. 4 and in Algorithm 1, the same U-Net is applied twice, once before and once after PD. An alternative design choice could consist of two separate, identical U-Nets that do not share weights and optimized individually with an identical parameter setup. Table 5 shows the result of the described ablation. With PSNR of 26.498 dB, optimizing two separate U-Nets is significantly worse than optimizing the single U-Net that has been applied twice. The intuition
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Table 5: Two-UNet ablation: Weight sharing across both stages improves performance over using two inde-
pendently trained U-Nets.
Method
Blind144 PSNR1
KernelFusion (Two separate U-Nets)
26.498
KernelFusion (same U-Net applied twice)
27.191
behind applying the same U-Net twice can be described as follows: Once the target prediction is sufficiently good at small ('s, the U-Net output difference between dnp at L + 1 (before PD) and t (after PD) should be marginal as the same images will have the same patch distribution (also compare Fig. 21). On the other side, we initialize Phase 2 with bicubic guess of for 2o- Due to the high noise level, PD destroys global structure while adjusting the patch distribution and the second application of the U-Net receives a heavily corrupted input. During this early phase, the first application of the U-Net effectively acts as regularizer that leverages the bicubic guess to provide the global structure information.
D RECEPTIVE FIELD OF PATCH DIFFUSION NETWORK
As discussed in Sec. 4 and Sec. PD operates with a receptive field of 15 pixels. Consequently, PD learns local structure at the patch level and has no explicit notion of global image layout. When predicting dg large (high noise levels), this can cause the reconstruction to lose the exact global structure of the image. Fig. 21 illustrates this: for small i, the noised image still preserves the global structure, and PD produces a reasonable reconstruction. However, for large (c.g., t 800), the input to PD is heavily corrupted, and PD reconstructs image whose local patches match the learned LR patch distribution, but the global structure becomes strongly blurred and inconsistent, yielding mosaic of plausible local patches. This effect diminishes t decreases and more of the original structure remains visible. Introducing a U-Net as a global image prior compensates for this lack of global awareness, allowing us both adjust the patch distribution and recover an accurate reconstruction.
E RUNTIME IMPROVEMENTS
As pointed out Limitations in Sec. 5, KernelFusion has to be trained from scratch for each image individually and hence comes with training cost that is reflected in runtimes that longer than other SOTA SR algorithms. While KernelFusion is not yet fast enough for commercial deployment, it serves a different purpose: establishing the scientific feasibility of a task previously considered impossible; Blind-SR with unrestricted kernels.
That said, optimization is a logical next step. Table shows the SR PSNRs using patch diffusion model trained for 100k steps as well as the 600k setup used for our main evaluation. With just 100k steps, patch diffusion can capture much of the necessary statistics. This yields a 4x speedup (~ minutes compared to 20 minutes) with negligible performance loss (~0.07 dB).
As runtimes for KernelFusion are above commercially deployed algorithms, two points shall be additonally stressed:
(i Breaking Assumptions: As shown in Fig. 1, SOTA methods rely on fixed priors (Gaus- sian/Motion) and collapse when these assumptions break. Our paper points out this general lim- itation and brings it to the attention the community. KernelFusion succeeds in this "impossible" regime by extracting the prior directly from the LR test image. We note that other single-image / internal-learning methods (c.g., KernelGAN Bell- Rell-Kligler al. (2019), MLMC Xia et al. (2024), DKP Yang et al. (2024b)) also require per-image optimization and typically take several minutes per image to produce their SR output. Yet, none these can handle arbitrary downscaling kernels.
(ii) Feasibility: We parallel to early foundational works like NeRF Mildenhall al. (2021) or Deep Image Prior Ulyanov et al. (2018), which required significant computation to establish feasibility in new domains. By proving that unrestricted kernel recovery is solvable, KernelFusion
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XY coords
Kernel Network INR
Estimated LR
Estimated HR THR
LR
Figure 9: Illustration of the kernel estimation in Phase 2. The INR-based kernel network maps normalized (ar, y) coordinates to kernel values, producing a downscaling kernel that is convolved with the current HR estimate and downsampled by a factor to yield the predicted LR image JLR-
Table Runtime improvements: Training PD for 100k steps instead of 600k steps leads to marginal losses in PSNR.
Method
Blind144 Runtime PSNR
min!
KemellFusion (PD: 100K)
27.117
KernelFusion (PD: 600K)
27.191
~ 20
opens new, free from predefined kernel assumptions paradigm. We hope that the community will build these foundations bridge the gap to real-time efficiency.
F DETAILS ON KERNEL ESTIMATION PHASE 2.
Given the current HR estimate ÍHR and the INR-based kernel network INRa, represent the down- scaling kernel on grid (in our experiments = 24). each normalized kernel coordinate g evaluate
kg IN
(3)
To obtain valid kernel, enforce non-negativity and unit sum. Using this kernel, the predicted LR image ÍiR is obtained by convolving the current HR estimate with ho and then downsample by the scale factor (here s 4):
[ (JHR * ko) tas
(4)
where denotes subsampling by and represents discrete convolution.
The patch-diffusion model in Phase was trained on the observed LR image ILR. Therefore, in Phase 2 we enforce consistency between the predicted LR image and the original observed LR image via an MSE loss
Lcons
||
IIK l
(5)
which couples the HR estimate fuR and the kernel parameters through the forward model. Figure illustrates the kernel estimation process.
G USE LARGE LANGUAGE MODELS
Large Language Models (LLMs) have been used while writing the paper i.e. to identify typos, im- prove formulations or shorten text snippets.
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13
GT Kemels
Figure 10: Estimated kernels of KernelFusion Blind144: Complete overview of all 144 esti- mated kernels.
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Real Image
MAXIFY
Estimated Kernel
88
Loas Quaino Tas
Velvabos
88
toiiiin Cosk
Bicubic
SinSR
SwinIR
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DIFFBIR
DCLS
RealDAN
Ours
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
SEA
Scar
Figure 11: Super-Resolution of REAL image (taken from Lai et al. (2016)).
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
TODAY WILL DO WHAREN S BRUORROW IAAN DO WHAT QUSERS CAN'T
Estimated Kernel
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
WH
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
OTH OM
Figure 12: SR of REAL image (captured using DSLR camera without optical stabilization).
(Top) The real image (used the LR input) & its estimated SR-kernel (using method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
Estimated Kernel
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Bicubic
SinSR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Figure 13: Super-Resolution of REAL image (taken from Levin et al. (2009)).
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
Estimated Kemel
Bicubic
SinSR
SwinIR
StableSR
NTE L
m T
NUTER
DIFFBIR
DCLS
RealDAN
Ours
VOTLS C
VETES
Bicubic
SinSR
SwinIR
StableSR
APOO'S
CEVOLLE
CHRCKIS
DIFFBIR CIVONRS
DCLS
ReaIDAN
Ours
CPPOSES
OPPORES
Figure 14: SR of REAL old (poor-quality) historic photo downloaded from the internet.
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There NO ground-truth HR image)
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Real Image
Estimated Kernel
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Figure 15: SR of REAL image (captured using a DSLR camera without optical stabilization).
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
Estimated Kernel
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Figure 16: Super-Resolution of a REAL image (taken from Levin et al. (2009)).
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
Estimated Kernel
NO SNIKKING WAET MIN 50 FEET
Bicubic
SinSR
Swin
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Bicubic
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StableSR
NOS NOS
NOS
NOS
WUT
WIT
WTT
AMATT
DIFFBIR
DCLS
RealDAN
Ours
NOS
NOS
NOS
NO WIT
S
MATT
WUTI
Figure 17: Super-Resolution of REAL image (taken from Lai et al. (2016)).
(Top) The real image (used the LR input) & its estimated SR-kernel (using method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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Real Image
Estimated Kernel
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Bicubic
SinSR
SwinIR
StableSR
DIFFBIR
DCLS
RealDAN
Ours
Figure 18: Super-Resolution of REAL image (taken from Lai et (2016).
(Top) The real image (used as the LR input) & its estimated SR-kernel (using our method).
(Middle & Bottom) A visual comparison of SRx4 results of leading SR methods. Zooms of the red and green image regions are displayed, respectively. (There is NO ground-truth HR image)
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INR
Direct Sigmoid
Direct Relu
Linear CNN
Figure 19: Estimated kernels for KernelFusion setup with different kernel estimation ap- proaches: INR, direct kernel estimation with sigmoid activation, direct kernel estimation with ReL.U activation, and linear CNN inspired by KernelGAN.
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Kernels
INR
Direct Sigmoid
Direct Relu
Linear CNN
Figure 20: Estimated kernels for the DIP setup with 4 different kernel estimation approaches: INR, direct kernel estimation with sigmoid activation, direct kernel estimation with ReL.U activation, and linear CNN inspired by KerneIGAN.
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Input
Noised
Reconstruction
800
400
t= 200
100
t 10
Figure 21: Prediction of 2o using Patch Diffusion: At high noise levels corresponding to large l's patch diffusion struggles to maintain global structure, and produces a mosaic-like reconstruction of local patches (best viewed zoomed in).
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Reviews:
[{"review_id": "k2med4L1yO", "reviewer": "Reviewer_xCF5", "summary": "This paper proposes KernelFusion, a zero-shot blind super-resolution method that simultaneously estimates an image-specific degradation kernel and the high-resolution image using a patch-based diffusion model. It addresses the limitation of existing methods that fail on complex, non-Gaussian kernels by leveraging internal learning, avoiding out-of-distribution problems.", "questions": "see weaknesses", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The combination of internal patch learning via diffusion models with implicit neural representations for kernel estimation is novel and creative.\n\n- Successfully handles complex, non-Gaussian kernels where state-of-the-art methods fail, pushing blind SR into a more assumption-free paradigm.\n\n- Strong experimental results on both synthetic kernels and real-world images convincingly demonstrate the advantage.", "weaknesses": "1. **Computational Cost and Practicality:** The most significant weakness is the computational cost. A 20-minute training time per image on a high-end GPU (L40S) makes it impractical for any real-time or even interactive application. While the authors correctly state their goal is to establish feasibility, this limitation is severe and should be a central point of discussion. Comparisons to other methods should ideally mention their relative runtimes to provide context.\n\n2. **Limitation to Global Kernels:** The method is built on the assumption of a single, globally uniform kernel. As noted in the limitations, this prevents it from handling spatially varying blur, which is a common and important problem in real-world scenarios (e.g., motion blur in parts of an image, lens aberrations). This restricts the scope of its applicability.\n\n3. **Ablation on Kernel Estimation Component:** While the ablation study in Table 3 effectively dissects the contributions to the final HR reconstruction quality (PSNR), it does not explicitly ablate the kernel estimation component. How crucial is the INR architecture compared to a simpler parameterization? A quantitative analysis (e.g., using kernel PSNR or MSE) of the estimated kernels in the different ablated settings would strengthen the claim that the INR is key to recovering complex kernels.\n\n4. **Comparison to Other Zero-Shot Methods:** The comparison to the two-step process of KernelGAN+ZSSR is excellent and shows a clear advantage. However, it would be even more compelling to see a comparison against other recent internal-learning or zero-shot SR methods that are not based on diffusion models, to better isolate the benefit of the proposed diffusion-based approach.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RxRJPrwdHy", "reviewer": "Reviewer_TT8b", "summary": "This work proposes KernelFusion, which primarily focuses on accurate estimation of non-restricted SR kernels to effectively tackle blind SR problems. In the first phase of KernelFusion, it learns local patch distribution of a single LR image with a zero-shot PatchDiffusion (PD) model, by optimizing PD at test time. After PD is sufficiently trained, it is frozen and acts as a strong prior for patch similarity across different scales. In the second phase, the SR result and according SR kernel is simultaneously estimated, with each an UNet and an INN. The method effectively captures extreme non-gaussian SR kernels, and outperforms baselines under various blind SR settings.", "questions": "**Question 1: Confusing experimental setting**\n\nThe experimental configuration of **Ablation (iii, PD+UNet)** is confusing.\nDoes *“acting as a denoiser”* indicate that the UNet is used only once (before the reverse diffusion step by PD)?\nIn other words, is this configuration equivalent to using **line 15 of Algorithm 1** only, while skipping **line 20 of Algorithm 1**?\n\nIf this interpretation is correct, the reviewer suggests adding another ablation experiment: skipping **line 15** while *not* skipping **line 20**. This experiment would help validate the necessity of applying the UNet twice, while also addressing the concern mentioned below:\n\n> “Due to the small receptive field, the network does not know global structure, effectively destroying it …” (Line 430)\n\n---\n\n**Question 2: Necessity of using a shared UNet**\n\nKernelFusion employs the same UNet twice (once before and once after PD).\nPlease discuss (and experimentally compare if possible) a configuration that uses independent network weights for each UNet step.\n\n---\n\n**Question 3: KernelFusion is slow**\n\n> *\"Our aim is not to deliver a production-ready Blind-SR system, but to establish feasibility of unrestricted kernel estimation ... \"* (Line 123)\n\nKernelFusion currently requires approximately **20 minutes** to perform SR for a single image, which remains excessively slow in practice: a clear limitation. However, the reviewer agrees with the academic necessity of analyzing unrestricted kernel estimation (despite being slow) and also considers the statement above fair.\n\nHowever, please discuss (and experimentally compare if possible) configurations that reduce the number of diffusion steps (or explore techniques designed to accelerate diffusion processes).", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "- The overall writing is very clear and easy to follow, with well supported citations.\n- The core idea is both intuitive and sound.\n- The performance gain is significant for unrestricted complex kernels (e.g., Blind144, DIV2KFK).\n- The method does not require pretraining, and thus, can adapt to arbitrary kernels.", "weaknesses": "The reviewer sincerely appreciates the authors’ efforts in this work. In its current state, I lean toward a borderline reject due to the weaknesses below. However, **I am willing to revise my evaluation to accept if these concerns are adequately addressed**. Please, counter-argue about my concerns and provide according experimental results.\n\n---\n\n**Weakness 1: Limited performance on conventional kernels**\n\nIn Table 2, the performance gain of **KernelFusion** is significant for *Blind144* and *DIV2K-FancyKernels (DIV2KFK)*. Since these test sets include extreme kernels (e.g., K0, K1, K2 in Fig. 5), these results align well with the aim of the paper: accurately estimating extreme **unrestricted** kernels.\n\nHowever, **KernelFusion** shows limited performance on *DIV2K-RK*, which uses random Gaussian kernels. Considering that such kernels are more common (and thus more practical), I have concerns about the performance of **KernelFusion** in real-world use cases. Because **blind SR** primarily focuses on practical scenarios (as bicubic SR tasks), this limitation is critical.\n\n---\n\n**Weakness 2: Missing analysis for the choice of INR**\n\n> *“We suspect that this limitation stems from the implicit bias of the CNN and MLP architectures (Line 105).”*\n\nOne of the key contributions of this work lies in the use of **INR architectures** to estimate complex non-Gaussian kernels. However, an analysis justifying this architectural choice is missing. It is necessary to include both (1) the final SR performance and (2) the kernel estimation results under alternative architectural designs for kernel estimation.\n\nThe reviewer suggests reporting SR performance and kernel estimation results\n\n* for the extreme kernels K0, K1, and K2 (shown in Fig. 5), and\n* under various architectural configurations, including (1) direct kernel optimization and (2) DIP-style architectures.\n\n---\n\n**Weakness 3: Lack of comparison with diffusion-based kernel estimation methods**\n\nAccurately estimating complex kernels with diffusion models **without any prior (i.e., pretraining)** is an interesting aspect of this work. However, kernel estimation using diffusion models is **not entirely new**. Prior diffusion-based works are not sufficiently discussed in this paper.\n\nFor instance, **BlindDPS [1]** employs diffusion models to estimate non-linear kernels for solving arbitrary blind inverse problems. The reviewer highlights the need to compare and discuss this work in two respects:\n* Although blind **SR** is not directly addressed in *BlindDPS*, extending it to SR is straightforward, as it only requires an additional subsampling step.\n* The central objective of both works is accurate kernel estimation using diffusion models.\n\nThe reviewer recommends comparing **KernelFusion** with *BlindDPS* (and possibly other related works), both theoretically and experimentally.\n\n[1] Chung, Hyungjin, et al. “Parallel diffusion models of operator and image for blind inverse problems.” *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, 2023.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "U0CxPDauzE", "reviewer": "Reviewer_cUZR", "summary": "This paper lacks sufficient motivation and fair evaluations. The proposed method tends to resolve complex kernel, however, the simulations are carried on unfair settings. The complex kernels are not real in application.", "questions": "See weaknesses", "limitations": "", "rating": 2, "confidence": 5, "soundness": 1, "presentation": 2, "contribution": 2, "strengths": "The paper is well-written and organised in a good structure.", "weaknesses": "1 This paper focuses on synthetic kernels (e.g., L-shape, empty squares in Fig. 5) with no evidence of their occurrence in real-world data. Why should the community care about reconstructing images degraded by a square kernel? The authors must justify whether such kernels exist beyond synthetic stress tests.\n2 Training a diffusion model for ​20 minutes per image​ on an L40S GPU is impractical for real applications (e.g., mobile or large-scale processing). The authors do not discuss trade-offs between cost and performance gains.\n​3  The authors claim diffusion models excel at capturing patch statistics but fail to compare against simpler internal-learning methods (e.g., GANs in KernelGAN). What advantages does diffusion offer over GANs for this task? The justification is weak.\n\n4 This paper omits critical details: How are the patch diffusion and INR networks initialized? What is the role of the \"consistency loss\" in Eq. 2? How does it interact with the diffusion prior? Why is a U-Net applied twice in Phase 2 (Sec. 4)? The ablation (Table 3) hints at its importance but lacks explanation. Kernel Estimation Stability: The INR-based kernel estimator is praised for flexibility but not evaluated for stability (e.g., sensitivity to noise or image content).\n\n5 The authors highlight performance on non-Gaussian kernels but ​ignore standard scenarios​ (e.g., isotropic Gaussian, motion blur). Does KernelFusion underperform on common kernels? Table 2 shows it is \"comparable\" on DIV2KRK (Gaussian kernels) but lacks head-to-head comparisons with SOTA methods like SwinIR or Real-ESRGAN in these settings.\n​6 On DIV2KFK and Blind144, KernelFusion surpasses SOTA methods by only ​0.1-0.3 dB in PSNR (Table 2), while bicubic interpolation outperforms many blind SR methods. Are these gains meaningful given the high computational cost?\n​7 Fig. 7 shows real-image results but without ground truth, making it impossible to assess accuracy. The kernels estimated for real images (e.g., DSLR without stabilization) appear unstructured—are they physically plausible?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "augCBRp8fI", "reviewer": "Reviewer_t2tb", "summary": "This paper introduces a zero-shot blind image super-resolution method that leverages a diffusion model to learn patch distribution and then further use it for kernel estimation and super-resolution. The overall approach contains two stages: patch diffusion training and blind super-resolution. In the second stage, an image-specific kernel is estimated with implicit kernel representation. In experiments, the proposed method is evaluated on three blind SR datasets with complex kernels.", "questions": "- The diffusion is trained with T=1000 steps, have you tried to use some acceleration algorithms such as DDIM to reduce the inference time?\n- In Eq. (1), the degradation is design without noise, but what if the LR image contains small noise?\n- How do you design the kernel size you want to learn in real world applications?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 1, "contribution": 2, "strengths": "- The proposed zero-shot training and inference is interesting, and the predicted kernels look good.\n- The results on Blind144 and DIV2KFK is promising.", "weaknesses": "Main weaknesses:\n- In Figure 2, the HR images are sent to the UNet twice at each iteration. The training and inference of diffusion model s also makes this algorithm inefficient. Could the authors provide a comparison on model complex and inference time?\n- Sec. 4 is not very clear to me, particular for the Phase 2. Could you rephrase it and provide a figure (or some math equations) for the kernel estimation part?\n- The experiments are only performed on x4 SR, it would be better to also evaluate the method on x2 or x8 SR datasets.\n- The written can be improved.\n- Small issue and suggestion: please use \"\\citep\" rather than \"\\cite\" for the citations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)