Blind Image Restoration via Fast Diffusion Inversion
Authors: Hamadi Chihaoui
Abdelhak Lemkhenter
Paolo Favaro
Venue: NeurIPS 2024 poster (2024)
Keywords: blind image restoration
diffusion models
unsupervised learning
Primary area: machine_vision

Abstract: Image Restoration (IR) methods based on a pre-trained diffusion model have demonstrated state-of-the-art performance. However, they have two fundamental limitations: 1) they often assume that the degradation operator is completely known and 2) they alter the diffusion sampling process, which may result in restored images that do not lie onto the data manifold. To address these issues, we propose Blind Image Restoration via fast Diffusion inversion (BIRD) a blind IR method that jointly optimizes for the degradation model parameters and the restored image. To ensure that the restored images lie onto the data manifold, we propose a novel sampling technique on a pre-trained diffusion model. A key idea in our method is not to modify the reverse sampling, i.e., not to alter all the intermediate latents, once an initial noise is sampled. This is ultimately equivalent to casting the IR task as an optimization problem in the space of the input noise. Moreover, to mitigate the computational cost associated with inverting a fully unrolled diffusion model, we leverage the inherent capability of these models to skip ahead in the forward diffusion process using large time steps. We experimentally validate BIRD on several image restoration tasks and show that it achieves state of the art performance.

Blind Image Restoration via Fast Diffusion Inversion
Hamadi Chihaoui Abdelhak Lemkhenter Paolo Favaro Computer Vision Group, Institute Informatics, University Bern, Switzerland (hamadi chihaoui, abdelhak. 1ennkenttrrrrrr paateeetterrrlllloo.. favaro)@unibbe... ch
Abstract
Image Restoration (IR) methods based on pre-trained diffusion model have demonstrated state-of-the-ar performance. However, they have two fundamental limitations: 1) they often assume that the degradation operator is completely known and 2) they alter the diffusion sampling process, which may result in restored images that do not lie onto the data manifold. To address these issues, we propose Blind Image Restoration via fast Diffusion inversion (BIRD) blind IR method that jointly optimizes for the degradation model parameters and the restored image. To ensure that the restored images lie onto the data manifold, we propose a novel sampling technique is not to modify the reverse sampling, i.e., not to alter all the intermediate latents, once an initial noise is sampled. This is ultimately equivalent to casting the IR task as an optimization problem in the space of the input noise. Moreover, to mitigate the computational model, we leverage the inherent capability of these models to skip ahead in the forward diffusion process using large time steps. We experimentally validate BIRD on several image restoration tasks and show that it achieves state of the art performance. Project page: tttps://haamen chihaoui gi thub. io/BIRD.
pre-trained diffusion model. A key idea in our method
associated with inverting fully unrolled diffusion
Introduction
Recent advances in generative learning due to the development of diffusion models [7, 18] have led to models capable generating detailed and realistic high-resolution images. In addition to their data generation capabilities, these models also provide an implicit representation of the distribution of the data they train on, which can be used for other applications, such as image restoration (IR). Indeed, several approaches have emerged to solve inverse problems using pre-trained diffussion models [8, 11, 21]. Those approaches start from a random noise vector as the diffusion input and introduce a projection after each diffusion reverse step enforce the consistency with the corrupted image. As shown by Chung [3] this procedure alters the original diffusion sampling process, and may cause the generated image to leave the data manifold during the iterative denoising process, which ultimately results in unrealistic image samples. Moreover, most of these methods are non-blind as they assume to have full knowledge of the degradation model, which is not practical in real-world applications.
To overcome all these challenges, we propose a novel blind image restoration method that jointly optimizes the degradation model parameters and the restored image only at test time (and thus separately for each new image). call this method BIRD, which stands for Blind Image Restoration via fast Diffusion inversion. Since BIRD does not need to pre-train model for the degradation operator, it can be used immediately on a wide range of IR tasks such as Gaussian deblurring, motion deblurring, super-resolus resolutin and denoising (see Figure 2). In this work, we show that having strong image prior and ensuring that the restored image never leaves the data manifold during the reconstruction process fundamental properties generalize problems. As shown in Figure 1, BIRD (see (f) to (i)) reconstructs realistic images at each iteration, while BlindDPS (see (b) to (e)) may initially reconstruct non realistic images. We observe that even
wide range of image degradation
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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(8)
(b)
(c)
(d)
(c)
8
(h)
Figure 1: Blind image deblurring with unknown motion blur. (a): blurry input image. From (b) (e): The top row shows the predictions of BlindDPS [1] as the iterations increase; the bottom row shows the corresponding estimated blur kernel. From (f) (i): Same estimates as in (b) (e), but obtained from BIRD, our proposed method. (j) is the ground truth sharp image (top) and ground truth blur kernel (bottom). Notice that BlindDPS [1] trains score-based model for the kernel estimation, while BIRD does not use any training and can adapt to any new kernel directly at test time. BIRD yields always natural images at every iteration of the reconstruction procedure. Finally, notice that despite recovering suboptimal blur kernel, the image reconstructed with BIRD is more similar to the ground truth image than with BlindDPS thanks to the robustness of our image generation procedure.
though we have more primitive blur reconstruction procedure (we directly regress the motion blur kernel), the reconstructed image is still more similar to the ground truth one (see column (I) than the final image estimate from BlindDPS (see (c) top). which uses a quite accurate blur kernel estimate (see (c) bottom). This speaks of the importance defining a strong image prior first and foremost.
To define the image prior, BIRD uses a pre-trained Denoising Diffusion Implicit Model (DDIM) [17] and exploits the existing deterministic correspondence between noise and images in DDIMs by casting the inverse restoration problem as a latent estimation problem, i.e., where the latent variable is the input noise to the diffusion model. In contrast to prior work, we do not alter the reverse sampling, ie., all the intermediate latents, once an initial noise is sampled. To then apply our image prior, we cast the IR task as an alternating optimization between the unknown restored image and the unknown parameters of the degradation model. However, direct implementation of the optimization procedure in the case a diffusion model used as a black box would be computationally demanding and ultimately impractical. To mitigate the substantial computational cost associated with inverting fully unrolled diffusion model, we leverage. for the first time in IR tasks, the inherent capability of these models skip ahead in the forward diffusion process using arbitrarily large time steps. We show that our method is able to achieve state of the art performance across a wide range of blind image restoration tasks. Our main contributions can be summarized follows
1. BIRD is the first to cast an IR task as latent optimization problem (where only the initial noise is optimized) in the context of diffusion models; our optimization procedure aims at generating images that lie on the data manifold at every iteration;
2. BIRD is computationally efficient; we propose a fast diffusion model inversion in the context of image restoration, without fine-tuning retraining;
3. We achieve state of the art results on CelebA and ImageNet for different blind IR tasks, such as Gaussian and motion deblurring, super-resolution, and denoising.
2 Related Work
Blind and non-blind image restoration methods. An image restoration task often cast as an inverse problem, where the degradation model is explicitly known. For example, in image deblurring the degradation model can be described by convolution with a blur kernel. Methods that explicitly assume the exact knowledge of the blur kernel are called non-blind methods. More general methods that assume only knowledge of the type of degradation (e-g., blurring), but not the values of its parameters, are instead called blind. Some recent examples of non-bll blind methods are [3] and DPS [2]. [3] points out that relying on an iterative procedure consisting of reverse diffusion steps and projection-basee
consistency step runs the risk of stepping outside of the data manifold, risk they mitigate using an additional correction term. DPS [2] proposes a more general framework to handle both the non-linear and noisy cases. DDNM [21] proposes zero-shot framework for

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Gaussian Deblur
Motion Deblur
Denoising
4x SR
er
er
Figure 2: We demonstrate BIRD several blind image restoration problems (i.e., when the values of the degradation model are unknown): Gaussian deblurring, motion deblurring, superresolution (SR) (it includes additional Gaussian blur) and denoising with an unknown noise distribution. BIRD applicable to single degraded image and does not require re-training or fine-tuning of the prior model (we use a diffusion model). Although some of the generated degraded images Gaussian blur, BIRD recovers a generic blur kernel (without making any Gaussianity assumption).
IR tasks based the range-null space decomposition. The method works by refining only the null-space contents during the reverse diffusion process, to satisfy both data consistency and realness. Some recent examples of blind methods are GDP [6] and BlindDPS [1]. GDP leverages DDPM and solve inverse problems via hierarchical guidance and a patch-basee method, BlindDPS proposes an extension of [2] the case of blind deblurring. They train a score-based diffusion model for the blur operator. At test-time, they jointly optimize for both the sharp image and blur operator by running the reverse diffusion process. However, training model for each new degradation operator can be time-comsee time-consuming. Fast Diffusion EM [9] proposes a method for blind image deblurring. It applies Maximization (EM) algorithm after each reverse diffusion step to jointly update the image latent and blur kernel. Gibbsddrm [13] extends DDRM [8] to the blind case by adopting Gibbs sampler to enable efficient sampling from the posterior distribution. In contrast to these works, in BIRD we introduce blind image restoration method based on a novel diffusion inversion for DDIM. Our method computationally efficient, as it requires only a few reverse diffusion steps, and generates realistic samples by only estimating the initial noise.
the Expectation pppectation-Maxxiiizattooo
Methods based on GAN inversion. Since our proposed method is based on inverting a diffusion process, we also briefly review related work in the literature and discuss how it differs from our approach. Because Generative Adversarial Networks (GANs) were among the best image generation models, number of methods [14, 15, 22, 23] inverts pre- rre-trained GANs to solve image restoration problems. DGPGAN [14] performs the GAN inversion on single new corrupted image. The authors shows that the inversion is not easily obtainable just with the direct optimization of the latent input to the frozen GANs model. Thus, they propose to also fine-tune the (unfrozen) GAN, while optimizing for the latent vector. [23] instead train encoder to invert pre-trained GANs

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(b)
(d)
Figure 3: Illustration of our proposed accelerated image sampling of the pre-trained DDIM. (a) intial noise 2т (0, (T 1000). (b), (c), (d), (e) and (f) samples zo generated using DDIMReverse(PT. ōl) with òl = 100, 50, 20, respectively. Notice how the generated images are all realistic regardless of the choice of the step size 81.
dataset of corrupted images (through masking). At test time they directly apply the trained encoder and the GANs on a new corrupted image without further training. BIRD shares the aim of inverting a generative model with the above prior work. However, as demonstrated in the literature for inverting GANs models, the inversion of generative models is far from a straightforward task. Moreover, the inversion of GANs and diffusion models are fundamentally different in nature. For example, while GANs generate samples in "one forward pass" diffusion models require multiple (denoising) steps. Also, all IR methods based GAN inversion either optimize the intermediate layers of the generator [4], train an auxiliary network (e.g., an encoder), or fine-tune the pre-trained GAN network. In our method, the diffusion model is not mnedtuned//raiee..
3 Image Restoration via BIRD
In this section, we introduce the classic Bayesian formulation of inverse problems applied to single degraded image. An important component in this formulation is the characterization of the image prior, which we do via DDIM diffusion models.
3.1 Problem Formulation
Image restoration (IR) can be cast as a Maximum Posteriori (MAP) optimization problem [24]
arg min log p(y]æ) + p(x),
(1)
where è E R2 is the restored image of size N₂ M2, pixels, y R N2x, the degraded image of size Ny My pixels, where (z) is the so-called likelihood and p(z) the prior distribution. Inverse problems describe IR tasks with degradation operator H, RMM, - N,N,M,, and noise image E RgN,xMM, such that the observed degraded image can be written as
Hz((x) + n.
(2)
7) is a vector with all the parameters that define the operator H,, IR tasks such as image denoising. deblurring and super-resolution can all be described using specific choices of H,, For instance, in the case of image deblurring, the H. operator can be described as a convolution with a blur kernel & such that (x) = A * æ, where denotes the convolution operation. In the blind deblurring problem, one assumes that H., takes the form of a convolution, but without knowing its parameters 7,, which, in this case, are the values of the true blur kernel k. Thus, also need to estimate the parameters n as part the optimization procedure. Only in the special case image denoising we use H, as the identity function. By assuming that the noise is zero mean Gaussian in the MAP formulation, one can rewrite eq. (1) as
â arg min ly (x) XR(x), MERNxxMa.N)
where R(x) is also called regularization term, and A > is coefficient that regulates the interplay between the likelihood and the prior. We define Ω2 E N.N.MM as the (compact) set of degradation- free (realistic) images and we propose employing formulation that implicitly assumes uniform

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Algorithm BIRD: Image Restoration
Require:
Degraded image step size 81, the dimension of x d = N₂ My. learning rate o, the stop threshold
Ensure: Return L0 Initialize 2 (0, and H with random parameters
2: while k + N and Lin(a Hat+) > E do
3: z = DDIMReverse( 8t)
4: TT = x. aV VV ( H(p))
5: 2T
k+1 ++
T Vd
6: 1y 11" afnfinlaa. Hax))
7: end while
8: return 20 = DDLMReverse(x2",00 8t)
Algorithm 2 DDIMReverse ( (TT 8t)
Require: Initial noise ZT ~ NO I), step size öt
I: = T
2: while l do
3: Pote (xt v1 (ne0 Vor
4: #t-5t var- + vI- āi-ōt. -l
20j
5: t öt
6: end while
7:
return Zo
prior p(x) = po (1) Qz. That is, R(x) lo)(pv())) log(c la (1)),, where is normalizing constant and 1o, (x) is 1 if r is in the support of 22 and 0 otherwise.
This results in the following simplified formulation
i, f = arg min 1 (x)11
To ensure that x E Pz. we parameterize x via the initial noise of pre-trained diffusion model 9 NaxM, + N trained by mapping noise samples from the high-density region of the standard Normal distribution (that we denote (2g) to the domain of degradation free (realistic) images Ωz In other words, we assume that Ω2 {g(=)) The optimization objective eq. (4) becomes then
ε, i arg min l1y H,(o()))11
(5)
=E0,..
with å = g(2). In high dimensions, N. N.M. || ~ E|zz 1 variance(2) = 1 as N, + In fact, most of the density high-dimensional Normal random variable is around ||=||² N, [12, 20]. Therefore, we propose approximate the original problem (3) with
f
arg min
|| - H,((()))
(6)
z =||==|==No NN.
3.2 An Efficient Diff'usion Inversion
In problem (6), we implement the function g by adopting pre-trained diffusion model. We choose the Denoising Diffusion Implicit Model (DDIM) [17] and set as fully deterministic diffusson process. To solve problem (6), we propose an optimization-baser iterative procedure. We jointly estimate a realistic image (i.e., with a high p(z)) and the forward degradation model H,, such that Hx)()) s3 y. In order find x, we explicitly exploit the correspondence between image samples and their associated initial latent image in DDIMs, in contrast to the mappings used in prior work [8, 11, 21]. Thus, we aim to find the initial noise sample that can generate the image x when applied to DDIM. To keep the notation consistent with the DDIM formalism, we denote images with To and the samples with IT, where T is the number of iterations the diffusion model. To make presentation self-contained, we briefly revise the notation and notions of diffusion models.
5

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er
er
Original
Reconstructed (PSNR=44. 10 1.06)
Original
Reconstructed
(PSNR=42 43 0.67)
Figure 4: Reconstruction results using BIRD on samples from CelebA and ImageNet validation datasets. The PSNR mean and standard deviation computed over 10 runs.
3.2.1 Background: Denoising Diffusion Probabilistic and Implicit Models
Denoising Diffusion Probabilistic Models (DDPM) [7] leverage diffusion processes in order to generate high quality image samples. The aim is to reverse the forward diffusion process that maps images to noise, either by relying a stochastic iterative denoising process or by learning the explicit dynamies of the reverse process, e-g., through an ODE [17]. More precisely the forward diffusion process maps image zo p(x) to zero-mean Gaussian æт ~ (O, I) by generating intermediate images z; for E [1,7] which are progressively noisier versions of zo- DDPM [7] adopts a Markovian diffusion process, where 2; only depends on 2T-1. Given non-increasing sequence a1:1 E (0, 1], the joint and marginal distributions of the forward diffusion process are described by
-N (Vansin (1 oz -1))1
II (()((111)), where (( N t=1
which implies that sample 2; simply by conditioning 2o with ãe IILsc as via
q (z)) . (Vāazzo (1 a))l.
(8)
To invert the forward process, one can train a model ca, with parameters 0, to minimize the objective
min
|||e calvor + ví -1-aa vā,ā,e, 0
Given the initial noise IT, image samples zo are obtained by iterating for E [1, the denoising update
2t co(os, x (1 - (1+0+) VI ai
Ft-1 Vai
+ 022,
(10)
with 2 ~ I), and of
1-ā:-1 (1 (1)).). 1-a;
The authors of [17] point out that the quality of generated images improves as the total number of denoising steps T increases. Thus, the inference loop using (10) becomes computationally expensive. To reduce the computational cost, they propose use instead
((*1rr/z)) (xo) q(>r|=0) II (
(11)
Denoising Diffusion Implicit Model (DDIM) [17], which foregoes the Markovian assumption in favor of a diffusion process where g(xr|æ0) = /V ( Varzu, (1 (1-av) (1-ar)1) and
-.-i - ooe. (2t - varzo) g( 1x,,,00) N/( -V(VaL-180 + v
(12)
VI ae

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L.R
GDP [6]
BlindDPS [1]
BIRD
GT
Qualitative comparisons of 4x SR on ImageNet. Each column shows examples. From left to right: input low-resolution images, GDP [6]. BlindDPS [1]. BIRD (our method), and the ground truth (GT) high-resolution and noise-free image.
Figure 5:
When a; = 0 for all f, the diffusion process is fully deterministic. This means that when we start from the same noise sample JT obtain the same generated image sample. Given de, one can first predict the denoised observation So, which a prediction of xo given æt.
(xt
vI dgep Cree((2 t))
to
(13)
V
Then, can predict - from and in using eq. (12) by setting or 0
Iz-1 = vā + v1 شر
(14)
with a 2:- 2n
Vi-a. direction pointing to zt. [17] shows that this formulation allows DDIM to fewer time steps inference by directly predicting Σz-; with which results in more computationally efficient process using
Lt- va + VI Cr-WW.
(15)
3.2.2 Accelerated DDIM Sampling
As previously mentioned, we adopt DDIMs our pre-trained generative process. Here, we explore the advantage of DDIMs of allowing fewer steps than in other diffusion models during the sampling process, as discussed in section 3.2.1. We start from ØT (O, Instead of denoising FT iteratively for all the steps used in the pre-training, we make larger steps by using intermediate estimates of cojz from 2, using the pre-trained DDIM model eq via
VI Crea (E
Eajt
(16)
Vāz
We define the jump to estimate -t-5t from Zoj; and using
ôt that controls the number of denoising steps, and can directly
var-s + VI āq-ōt. St Vor
(17)
V1
A larger step size öt allows us to favor speed, while lower one favors precision or fidelity. This itera- tive procedure, which we summarize in Algorithm 2, results an estimate of xo that differentiable in Sr. We denote by DDIMReverse(, 5() the mapping function between 2r and that is parameter- ized with the step size 8t (this essentially our choice of g problem (6)). Figure shows sampled images 2o using different öt starting from the same initial noise zT through DDIMRevers((, 6t).
7

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Blurry
GDP [6]
BlindDPS [1]
BIRD
GT
Figure 6: Qualitative comparisons of Gaussian deblurring on CelebA. From left to right: input blurry
image, GDP [6], BlindDPS [1], BIRD (our method), and the ground truth sharp image.
Noisy
DIP [19]
BIRD
GT
V
VE
Figure 7: Qualitative comparisons of image denoising CelebA. From left to right: input noisy image, GDP [6], BlindDPS [1]. BIRD and the original image (GT).
3.2.3 BIRD: Blind Image Restoration via Fast Diffusion Inversion
BIRD performs an iterative minimization of problem (6) with a running index k, which we append as superscript to the estimated unknowns. It starts from initial noise instance x² (O(0, I) and parametric degradation model Hy,, where 17 is randomly initialized. At each iteration k we first compute our estimate of the clean image z by mapping z4 through DDIMReverse(,,.
S DDIMMeeerse
(18)
We then compute the restoration loss
LIR (2) H,,) (1y) 1,,-H,(,,)11
(19)
Given an initial noise 2 and Hyr, the optimization iteration is simply derived through gradient descent with a learning rate a
k+1 = a (1 Hygh) and - H²r))
(20)
To impose the normalization constraint on or we set its Fuclidean norm to || = VN, M, via
k+1
NN,M,.
(21)
After N iterations, or when (x Hy,) becomes small enough, we deem that BIRD has converged. The restored image âg is then generated by 2o = DDIMRevvrss((2), St), which always ensures that to is within the manifold of realistic images, already shown in Figure 3. Moreover, in Figure 4 show two examples of the reconstruction with (x) = z and with un-corrupted woise-free images from the validation dataset of ImageNet [5] and CelebA [10]. We summarize this iterative procedure in Algorithm
Experiments
4.1 Image Restoration Tasks
We showcase BIRD on four different image restoration tasks: Gaussian and motion deblurring, denoising, and image super-resolution (SR), For Gaussian deblurring, anisotropic Gaussian

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Table 1: Quantitative evaluation of several inverse problems on the CelebA validation dataset. The best and second best methods are indicated in bold and underlined respectively.
Method
Motion Deblur
Gaussian Deblur
8x SR
Denoising
PSNR 1 LPIPS
PSNR t LPIPS
PSNR
LPIPS & PSNR 1 LPIPS
BlindDPS [1]
23.15
0.281
23.56
0.257
21.82
0.345 0.415
DIP [19]
18.64
24.57
0.282
Fast Diffusion EM [9]
23.18
0.284
24.52
0.235
GibbsDDRM [13]
22.94
0.314
23.57
0.266
DGPGAN [14]
22.23
0.304
20.65
0.378
19.83
0.372
GDP [6]
22.49
0.314
22.53
0.304
20.78
0.357
BIRD
23.76
0.263
24.67
0.225
22.75
0.306
28.46
0.227
Table 2: Quantitative evaluation of several inverse problems on the ImageNet validation dataset. The best and second best methods are indicated in bold and underlined respectively.
Method
Gaussian Deblur
4x SR
PSNR f
LPIPS
PSNR f
LPIPS
BlindDPS [1]
24.28
0.296
21.36
0.374
DIP [19]
18.67
0.456
DGPGAN [14]
21.67
0.384
19.58
0.461
GDP [6]
22.45
0.368
20.24
0.435
BIRD
23.76
0.321
22.15
0.354
kernel. We follow the procedure described in [16] and use the same feed-forward network for the kernel estimation. For all tasks, we note that we consider the noisy case with noise standard deviation of 0.05. For image denoising, we introduce a combination of Gaussian signal-independeen and speckle degended))))dnn) noises simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. For all our experiments, we use ôt 100 and a maximum number of iterations N 200. Adam is adopted as optimizer with 0.003 learning rate. We evaluate our method both on the validation datasets of ImageNet [5] and CelebA [10] at 256 x 256 pixel resolution. We follow [2, 3] and report the obtained LPIPS [25] and PSNR for each experiment.
4.2 Qualitative Results
Figures 5, 6, show non cherry-picked examples of ImageNet and CelebA images restored in the cases of 4x super-resolution, Gaussian deblurring and denoising. We also compare our work with GDP [6] and BlindDPS [1]. BIRD seems to recover always more realistic, consistent and accurate images than the other competing methods.
4.3 Quantitative Results
Tables 1 and report the performance of BIRD as well DIP [19], DGPGAN [14], DPS [2], GDP [6] for CelebA and ImageNet, respectively. For both datasets, we observe that our method achieves state of the results both in terms of PSNR and LPIPS metrics.
4.4 Ablations
We also compare the runtime performance of BIRD to other state-of-the-art methods and evaluate the impact of the step size öt. All experiments are carried on a GeForee GTX 1080 Ti. Effect of the step size 5t: The step size öt defines a trade-off between speed and accuracy. Table shows the PSNR. LPIPS and runtime for image denoising on CelebA. We observe that the reconstruc- tion accuracy of BIRD is not too sensitive to this parameter, while the runtime is linearly affected. 81. 100 gives good trade-off between the speed and the reconstruction accuracy.
Memory usage and Computational Cost: In Table 4, we report the memory usage and the runtime per image of different blind deblurring methods. We also show as a reference Naive Inversion, which performs the inversion by unrolling all the steps of the pre- pre-trained diffusion model. This case

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Table 3: Effect of the step size öt on the visual quality and the runtime of denoising on CelebA.
Table 4: Runtime (in seconds per pro-
cessed image) comparison of blind deblur- ring methods on CelebA
Step size (ôt)
PSNR 1
LPIPS |
Time[s] J
Method
Time[s]
Memory [GB)
50
28.74
0.218
412
100
28.67
0.224
234
DGPGAN [14]
190
0.9
200
28.45
0.237
110
GDP [6]
118
1.1
Naive Inversion
5700
2.2
BlindDPS [1]
270
6.1
BIRD
234
1.2
shows how BIRD results in a significantly faster execution. Despite being an iterative method, BIRD has reasonable runtime making practical IR method. The reported speed uses öt 100.
4.5 Limitations and Broader Impacts
We have evaluated our method on degradation operators with given explicit parametrized form (albeit with unknown parameters). It would be interesting to further investigate the use of BIRD on problems where an explicit form of the degradation operator is difficult to have, such as in image deraining and dehazing. In terms of broader impacts, BIRD leverages pre-trained denoising diffusion models with both their advantages and pitfalls. It takes advantage of their strong prior, but may also be affected by their data- inta-induced biases.
Conclusion
We have introduced BIRD, novel robust, accurate and fast framework for solving general blind image restoration tasks by using pre-trained diffusion generative models as learned priors. Our method exploits the deterministic correspondence between noise and images DDIM by casting the inverse restoration problem networks on specific task, but can instead directly applied new images and new degradation models. We leverage the capability of DDIM to skip ahead in the forward diffusion process and provide an efficient diffusion inversion in the context of image restoration. We demonstrate that BIRD achieves state of the art performance blind image restoration tasks including Gaussian deblurring, motion deblurring, super-resolution and denoising.
latent estimation problem. Our framework does not require training
Acknoweledgements. We acknowledge the support of the SNF project number 2000202200300
References
[1] Chung, H., Kim, J., Kim, S., Ye, J.C.: Parallel diffusion models of operator and image for blind inverse problems. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 6059-6069 (2023) 3, 7, 8, 9, 10
[2] Chung, H., Kim, J., Mccann, M.T., Klasky, M.L., Ye, J.C.: Diffusion posterior sampling for general noisy inverse problems. arXiv preprint arXiv:2209. 22:.:229991147 (2022) 2, 13
[3] Chung, H., Sim, B., Ryu, D., Ye, J.C.: Improving diffusion models for inverse problems using manifold constraints. In: Oh, A.H., Agarwal, A., Belgrave, D., Cho, K. (eds.) Advances in Neural Information Processing Systems (2022), htt0:///ttt////o/ooor/////////// nJJjvOJDJju 1, 2.9
[4] Daras, G., Dean, J., Jalal, A., Dimakis, A.G.: Intermediate layer optimization for inverse problems using deep generative models. arXiv preprint arXiv:2102.07364 (2021)
[5] Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: Imagenet: A large-scale hierarchical image database. 2009 IEEE conference on computer vision and pattern recognition. pp. 248-255, Icee (2009) 8,9
10

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[6] Fei, B., Lyu, Z., Pan, L., Zhang, J., Yang, W. Luo, T., Zhang, B., Dai, B.: Generative diffusion prior for unified image restoration and enhancement. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 9935-9946 (2023) 3, 7, 8, 10
[7] Ho, J., Jain, A., Abbeel, P.: Information Processing Systems 33, 6840-6851 (2020) 1,
Denoising diffusion probabilistic models. Advances in Neural
[8] Kawar, B., Elad, M., Ermon, S., Song, J.: Denoising diffusion restoration models. arXiv preprint arXiv:2201.1 1793 (2022) 3,5,5
[9] Laroche, C., Almansa, A., Coupete, E.: Fast diffusion em: diffusion model for blind in- verse problems with application to deconvolution. In: Proceedings of the IEEE/CVF Winter Conference Applications of Computer Vision. pp. 5271-5281 (2024) 3, 9
[10] Liu, Z., Luo, P., Wang, X., Tang, X.: Large-scale celebfaces attributes (celeba) dataset. Retrieved August 15(2018), 11 (2018) 8, 9
[11] Lugmayr, A.. Danelljan, M., Romero, A., Yu, F., Timofte, R., Van Gool, L.: Repaint: Inpainting using denoising diffusion probabilistic models. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 1461-11471 (2022) 1,5
[12] Menon, S., Damian, A., Hu, S., Ravi, N., Rudin, C.: Pulse: Self-supervised photo upsampling via latent space exploration of generative models. In: Proceedings of the ieee/cvf conference on computer vision and pattern recognition. pp. -437-2445 (2020) 5
[13] Murata, N., Saito, K., Lai, C.H., Takida, Y., Uesaka, T., Mitsufuji, Y., Ermon, S.: Gibbsddrm: A partially collapsed gibbs sampler for solving blind inverse problems with denoising diffusion restoration. In: International conference machine learning. pp. 25501-25522, PMLR (2023)
3,
[14] Pan. X., Zhan, X., Dai, B., Lin, D., Loy, C.C., Luo, P:: Exploiting deep generative prior for versatile image restoration and manipulation. IEEE Transactions on Pattern Analysis and Machine Intelligence 44(11), 1),
(2021) 3,9, 10
[15] Poirier-Ginter Y., Lalonde, J.F.: Robust unsupervised stylegan image restoration. In: Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 22292-22300 (2023)
[16] Ren, D., Zhang, K., Wang, Q. Hu, Q.. Zuo, W.: Neural blind deconvolution using deep priors. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 3341-3350 (2020) 9
[17] Song, J., Meng. C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02500 (2020) 2, 5, 6,7
[18] Song, Y., Ermon, S.: Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems 32 (2019) I
[19] Ulyanov, D., Vedaldi, A., Lempitsky, V.: Deep image prior. In: Proceedings of the IEEE conference computer vision and pattern recognition, pp.
(2018) 8,
[20] Vershynin, R.: Random vectors in high dimensions. Cambridge Series Statistical and Proba- bilistic Mathematics. Cambridge University Press 3, 38-69 (2018) 5
[21] Wang, Y., Yu, J., Zhang, J.: Zero-shot image restoration using denoising diffusion null-space
model. The Eleventh International Conference on Learning Representations (2023) 1,
[22] Yang, T., Ren, P., Xie, X., Zhang, L.: Gan prior embedded network for blind face restoration in the wild. In: Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pp. 672-681 (2021)* 3
[23] Yu, Y., Zhang, I.., Fan, H., Luo, T.: High-fidelity image inpainting with gan inversion. In: European Conference Computer Vision. pp. 242-258. Springer (2022) 3

---

[24] Zhang. K., Li, Y., Zuo, W., Zhang, L., Gool, L.V., Timofte, R.: Plug Blug-and-play and-play image restoration with deep denoiser prior. IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 6360-638 6376 (2020) 4
[25] Zhang, R., Isola, P., Efros, A.A., Shechtman, E., Wang, O.: The unreasonable effectiveness of deep features as a perceptual metric. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 586-595 (2018) 9
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Clean target not available.
Figure 8: BIRD also be applied to non-blind tasks. In particular, notice the special case of sparse-view CT image reconstruction (rightmost two columns), where the measurements are not in the image domain (on the top Measurements. Second row: BIRD reconstructions. Third row: Ground-truth data.
show the reprojections of the measurements). First row:
A Appendix supplemental material
A.1 Application of BIRD to non-blind cases
Naturally, BIRD can also be applied non-bind cases, i.e., when the degradation operator is completely known. In Figure 8, we show the application of BIRD to some non-blind image restoration tasks such as image inpainting and aparse-view CT image reconstruction.
A.2 Robustness of BIRD severe degradation
BIRD is also robust to severe degradation. In Figure 9, we show that BIRD is more robust in the case of face hallucination (x 16 super-resolution). BIRD outperforms the other methods terms of visual quality as well as faithfulness.
A.3 Robustness of BIRD to errors in the degradation operator estimate
Non-blind methods generally rely off-the-shelf methods estimate the degradation operator. These off-the-shelf methods are not 100% accurate. We simulate a small error in the degradation the simulated kernel (plus this error) generate the restored image for the non-blind DPS [2] and BIRD. As shown in Figure 10, BIRD produces better quality outputs compared the bon-blind method DPS when using the kernel with slightly simulated error.
operator and
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LR
DDNM
DPS
BIRD
GT
ITISH FILM A
ART
Angeles
Figure 9: Robustness to severe degradation (Face hallucination, x16 superresolution) BIRD is more robust to severe degradations than competing methods, both in terms of visual image quality and faithfulness.
Blurry
DPS
BIRD (ours)
Figure 10: Robustness errors in the degradation operator estimate. First column: ground-truth kernel (std=8.5) and a kernel with slightly simulated error (std=8). Second column: blurry images using the kernel with slightly simulated error. Third and fourth columns: Output of DPS and BIRD. Fifth column: Ground-truth.
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Reviews:
[{"review_id": "3mK5EjihUh", "reviewer": "Reviewer_gDW8", "summary": "The paper presents a method to accelerate blind image reconstruction by leveraging pre-trained diffusion models. The authors suggest a strategy that simultaneously optimizes the degradation model parameters and the restored image, thereby improving the reconstruction process’s efficiency.\n\nFurthermore, the authors introduce a sampling method based on a pre-trained diffusion model. This method is devised to ensure the restored images are in alignment with the image manifold, a critical factor in preserving the restored images’ integrity.\n\nTo enhance the speed of the process, the authors consider advancing in the forward diffusion process using large time steps, Thus they are able to significantly reduce the runtime of restoration process.\n\nThe experimental results demonstrate improved performance across various tasks, outperforming BlindDPS, a recent solution for blind inverse problems. Furthermore, it surpasses a couple of other blind image reconstruction methods that do not rely on diffusion models.", "questions": "- It would be beneficial to include the results of the version with δt=1 in Tables 1, 3, and 4 as well.\n    \n- The paper only qualitatively considers JPEG de-artifacting and compares it solely to DIP. Why are more recent methods such as the following not considered?\n    \n    - [1] “Towards Flexible Blind JPEG Artifacts Removal” by Jiang, Jiaxi, Kai Zhang, and Radu Timofte. *ICCV* 2021.\n        \n    - [2] “DriftRec: Adapting Diffusion Models to Blind JPEG Restoration” by Welker, Simon, Henry N. Chapman, and Timo Gerkmann. *TIP* 2024.\n        \n- Minor point:\n    \n    - In Figure 3, the image index should be corrected from (f) to (e).", "limitations": "no comments.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper demonstrates a significant improvement in speed and memory efficiency over the primary method, BlindDPS. Additionally, the quality of the reconstruction has also been enhanced.\n    \n- The method, in particular, is articulated and presented effectively in the paper.", "weaknesses": "- The paper lacks a theoretical discussion and experimental comparison with some recent or related blind diffusion methods for inverse imaging problems, such as [3-5].\n    \n    - [3] “Fast Diffusion EM: A Diffusion Model for Blind Inverse Problems with Application to Deconvolution” by Laroche, Charles, Andrés Almansa, and Eva Coupete. *WACV* 2024.\n        \n    - [4] “Gibbsddrm: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration” by Murata, Naoki, et al. *ICML* 2023.\n        \n    - [5] “A Diffusion Model with State Estimation for Degradation-Blind Inverse Imaging” by Ji, Liya, et al. *AAAI* 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see the detailed response below.\n\n\n### Q1. Theoretical Discussion and Experimental Comparison to [3-5]\n\n\n|   Method|   Zero-shot?| Task-agnostic?  |  Code available? |   |\n|---|---|---|---|---|\n| BIRD  | *Yes*  | *Yes*  |  N.A |   |\n|  [1] |  No | No  |  Yes |   |\n|  [2] | No  | No  | Yes  |   |\n| [3]  |  Yes | No  |  Yes |   |\n| [4]  |  Yes | Yes  | Yes  |   |\n| [5]  | No  | Yes  |  No |   |\n\n\n\nWe thank the reviewer for the suggestion. We will add the content below to the paper. First, let us discuss the references [3-5]. BIRD is a zero-shot method (no training involved), while [5] involves fine-tuning a diffusion model and training a state estimator. It also requires a dataset of input-output pairs for training, whereas BIRD does not. References [3-4] are zero-shot approaches, but  fundamentally different from BIRD. A key difference is that [3-4] *modify* the original diffusion sampling by adding a projection-based step to enforce consistency with the corrupted image. In contrast, in BIRD we use the original diffusion sampling scheme as is. Moreover, [3] applies the EM algorithm after each diffusion reverse step to jointly update the image latent and the kernel blur. [4] extends DDRM to the blind case by adopting a Gibbs sampler to enable efficient sampling from the posterior distribution. We note that [3] is task-specific (proposed only for blind deconvolution) while BIRD can handle different IR tasks. [4] can only handle linear IR tasks (BIRD can handle non-linear ones like JPEG de-artifacting) and is not easily applicable to problems involving linear operators for which the SVD is computationally infeasible.\nBelow we also show a quantitative comparison between BIRD and methods [3,4]. Unfortunately, we could not compare to [5] because we could not find code for it and the results in [5] is not directly comparable to our paper because of not using the exact degradation or noise model.\n\n\n|   **Method**|   Motion Deblur | Gaussian Deblur |   SR x8 | \n|---|---|---|---|\n|  [3] |  23.18/0.284 | 24.52/0.235  |  n.a | \n|  [4] |  22.94/0.314 | 23.57/0.266  |  22.17/0.357 |  \n|  BIRD | **23.76**/**0.263**  | **24.67**/**0.225**  |  **22.75**/**0.306** | \n\nQuantitative comparison (PSNR/LPIPS) on CelebA.\n\n\n\n### Q2. Comparison to [1-2]\n\nWe thank the reviewer for their suggestion. We did not include comparisons to methods [1-2] because BIRD is zero-shot and task-agnostic, while [1-2] are dataset-based (involving training) and task-specific (JPEG deartifacting). In our paper, we followed recent zero-shot works, such as [8, 9], which do not consider dataset-based approaches, as such a comparison is not an apple-to-apple. \n\nNonetheless, we compared to [1], which provides a pretrained model in their official code. Unfortunately, we could not compare to [2] as they do not provide a pretrained model and we could not train their model in time. We will include a comparison to [2] in our revision.\n\nIn the table below, we illustrate the key difference between zero-shot (single-image) and dataset-based methods. Dataset-based approaches tend to work well when tested with data having the same degradation operators/noise distributions seen during training, but their performance drops when dealing with new data. We further show this key difference in Figure 5 of the rebuttal PDF. In that Figure 5, we show that when testing [1] with no noise (the same as during training), it outputs a clean image. However, when adding a small amount of noise not seen during training, [1] produces artifacts. In contrast, BIRD yields the same result under both settings.\n\n|   **Method**|   **CelebA (w/o noise)**| **CelebA (w/ noise)** |  \n|---|---|---|\n|  [1] |  **29.24**/0.242 | 26.45/0.318  |  \n|  BIRD | 28.75/**0.221**  | **28.67**/**0.224**  |  \n\nQuantitative comparison (PSNR/LPIPS) on JPEG de-artifacting on CelebA\n\n### Q3. Include the Results of the Version with δt=1 in Tables 1, 3, and 4\n\nWe show below the updated Table 3. Running BIRD with δt=1 is computationally almost infeasible as one image take around 22500 seconds. Indeed, one of our motivations is to propose a fast (and computationally feasible) diffusion inversion that benefits from the ability to jump ahead in the diffusion reverse process (δt higher than 1). \nWe will add the results for some reasonably small δt (δt=10 or δt=20)  for other tables in our revision.\n\n(If the reviewer means the case with one jump (δt=1000), this is so feasible and we can add it.)\n\n|   step size (δt) |   PSNR ↑  | LPIPS ↓  |  Time [s] ↓ |   \n|---|---|---|---|\n|  δt=1 |  - | -  |  22500 |  \n|  δt=50 | 28.74  | 0.218  | 412  |  \n| δt= 100  |  28.67 | 0.224  |  234 |  \n| δt= 200  |  28.45 | 0.237  | 110  |  \n\nUpdated Table 3\n\n### Q4. In Figure 3, the image index should be corrected from (f) to (e)\n\nThanks for pointing this out. We will correct it in our revision.\n\n\n[8] Denoising Diffusion Restoration Models. Neurips 2022\n\n[9] Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model. ICLR 2023", "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": "8joTkAdlj3", "reviewer": "Reviewer_PrQF", "summary": "This paper proposed new blind image restoration (BIR) method by exploring the image prior induced by diffusion model (DM). Different from the existing DM-based methods, this work presents a diffusion inversion technique, such that the estimated image can be constrained to lie in the image manifold learned by the pre-trained DM, and the computational cost can be reduced. Experiments on several image restoration tasks have been conducted to demonstrate the effectiveness of the proposed method.", "questions": "It seems that Figure 1 indeed shows an example of deblurring with motion blur, while the caption says Gaussian blur.", "limitations": "The authors have discussed the limitations, which are reasonable.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The idea of diffusion inversion is interesting and reasonable, which broaden the concept of deep generative prior, and can possibly motivated more related studies.", "weaknesses": "The major problem is that the experiments are not comprehensive enough.\n\n- Some commonly used benchmarks in corresponding BIR tasks were not considered. For example, for the blind motion deblur task, commonly used Lai [1] and Levin [2] datasets were not used for evaluation.\n\n- Some advanced deep prior-based methods for corresponding image restoration tasks were not compared. For example, for the deblur task, some DIP-based methods e.g., [3][4][5], were not compared; for the super-resolution task, also some DIP-based ones, e.g., [6][7], were not included\n\nReferences:\n\n[1] W. Lai et al. A comparative study for single image blind deblurring. CVPR, 2016.\n\n[2] R. Köhler et al. Recording and playback of camera shake: Benchmarking blind deconvolution with a real-world database. ECCV, 2012.\n\n[3] D. Ren et al. Neural blind deconvolution using deep priors. CVPR, 2020.\n\n[4] D. Huo et al. Blind image deconvolution using variational deep image prior. TPAMI, 2023.\n\n[5] J. Li et al. Self-supervised blind motion deblurring with deep expectation maximization. CVPR, 2023.\n\n[6] J. Liang et al. Flow-based kernel prior with application to blind super-resolution. CVPR, 2021.\n\n[7] Z. Yue et al. Blind image super-resolution with elaborate degradation modeling on noise and kernel. CVPR, 2022.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see the detailed response below.\n\n### Q1. Add more comparisons [3-7]\n\n\n|   Method|   Zero-shot?| Task-agnostic?  |  Code available? |   |\n|---|---|---|---|---|\n| BIRD  | *Yes*  | *Yes*  |  N.A |   |\n|  [3] |  Yes | No  |  Yes |   |\n|  [4] | Yes  | No  | Yes  |   |\n| [5]  |  No | No  |  No* |   |\n| [6]  |  Yes | No  | Yes  |   |\n| [7]  | No  | No  |  Yes |   |\n\n\n\nWe thank the reviewer for the suggestion. BIRD is zero-shot and task-agnostic, while [4-7] are dataset-based (involving training) and [3-7] are task-specific. We followed recent zero-shot works, such as [8, 9], which do not consider dataset-based approaches, as such a comparison is not apple-to-apple. Nonetheless, we report the mentioned comparison in the following tables and will include them in our revision. Unfortunately, the inference script for [5] is not publicly available. We have contacted the authors and will include the comparison in a comment if we receive the scripts.\n\n|   **Method**|   **CelebA**| **Imagenet** |   **Lai[1]** | **Levin[2]**|\n|---|---|---|---|---|\n|  [3] |  20.12 | 19.15  |  21.13 |  33.07  | \n|  [4] |  21.43 | 20.45  |  **25.12** |  -  | \n|  BIRD | **24.67**  | **23.76**  |  24.57 | **34.18**  | \n\nQuantitative comparison (PSNR) on Gaussian Deblurring\n\n|   **Method**|   **CelebA**| **Imagenet** |  \n|---|---|---|\n|  [6] |  20.62 | 20.45  |  \n|  [7] |  22.38 | **22.53**  |  \n|  BIRD | **22.75**  | 22.15  | \n\nQuantitative comparison (PSNR) on Super-resolution\n\n### Q2. Benchmark on Lai [1] and Levin [2] Datasets for Blind Deblurring\n\nLai [1] and Levin [2] datasets are generally used for dataset-based [7] and task-specific methods like [3, 4, 5]. We followed the recent zero-shot and task-agnostic works (the same category as our paper) such as [8, 9], which benchmark on ImageNet and FFHQ/CelebA.\n\nIn the table above, we added a comparison on Lai [1] and Levin [2] for Gaussian deblurring. For [3] and [4], we report the results shown in their papers. We note that [4] did not compare on Levin [2].\n\n### Q3. Figure 1 shows an example of deblurring with motion blur and not Gaussian blur\n\nThanks for pointing this out. We will correct it in our revision.\n\n\n[8] Denoising Diffusion Restoration Models. Neurips 2022\n\n[9] Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model. ICLR 2023", "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": "XkBllQ0TZj", "reviewer": "Reviewer_ebAr", "summary": "The authors propose a novel approach to solving image restoration problems using diffusion models, termed BIRD. \nUnlike previous approaches, BIRD alternates between optimizing a parameterized forward operator and the initial latent variable of a DDIM to address various IR problems in a blind manner (i.e., with an unknown forward operator). This iterative process involves mapping the current latent variable to its outcome in the DDIM via the DDIMReverse algorithm and alternately taking a gradient step of the measurement error with respect to the current latent variable and the forward operator's parameters.", "questions": "How does the method work for general inverse problems? Does Algorithm 1 actually require the measurements to be in image space?", "limitations": "- The method is presented as superior to non-blind methods [2, 3], but these methods tackle more general inverse problems that do not require measurements in image space (e.g. sparse-view CT or phase retrieval). This difference should be emphasized.\n- It would be beneficial to know which problems cause the method to fail, at least in supplementary materials.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "This paper presents an original approach by leveraging pretrained diffusion models to address blind inverse problems in image restoration. The simplicity and novelty of the method lie in its creative combination of well-known techniques, making it a noteworthy contribution to the field. \n\nThe quality of the theoretical analysis, particularly in sections 3.2 - 3.2.2, is commendable as it is grounded in related work, providing a solid foundation for the proposed method. The results presented demonstrate the method's potential and effectiveness in addressing the stated problems.\n\nThe clarity of the paper is generally good, with the authors providing a comprehensive introduction and detailed descriptions of the algorithms. The inclusion of specific equations and theoretical justifications helps in understanding the underlying principles of the method. The paper's structure and flow, from the introduction to the results, are logically organized, aiding in the reader's comprehension.\n\nIn terms of significance, the method shows considerable promise for application in image restoration, particularly for more complex and challenging inverse problems. The differentiation from non-blind methods is an important aspect, and the potential for this method to address a wider range of problems enhances its relevance and impact in the field.", "weaknesses": "The paper has several areas that require improvement. The theoretical analysis in section 3.1 is noted to need thorough revision, suggesting that some foundational aspects of the method may not be as robust as they could be. Additionally, much of the theoretical content is heavily dependent on related work, which might limit the perceived novelty of the contribution.\n\nSpecific areas needing attention include:\n- The phrase \"better neural network architecture choices\" on lines 21-22 should be made more specific to avoid ambiguity.\n- Equations 1, 3, 4, 6, 8: \\DeclareMathOperator*{\\argmin}{arg\\,min}\n- Line 129: If a certain coefficient $\\rho$ is equivalent to Eq. 3, it should be easily expressible in terms of $\\lambda$.\n- Line 130: $g_*$ is not defined.\n- Lines 132-134: The wording and notation need clarification (e.g., $\\| z \\|^2 = N_x \\times M_x$, usually $\\| z \\|^2$ is a scalar, $N_x \\times M_x$ is a tuple) \n- The derivation of Eq. 8 seems out of place and might be better suited for section 3.2.3.\n\nThe clarity of the introduction could be improved as it currently reads too much like related work. The work of Chung et al. [2, 3] should be discussed separately in the related work section. Additionally, the statement about GAN inversion methods on lines 104-105 should consider other methods that optimize intermediate latent variables (e.g., https://arxiv.org/abs/1703.03208, https://arxiv.org/abs/2102.07364).\n\nAlgorithm 1 is confusing with its indices, and it is unclear whether $x_T$ or $x_0$ is the initial latent variable. Similarly, Algorithm 2 would benefit from including requirements similar to those in Algorithm 1 to enhance clarity.\n\nFinally, while the results are significant, the paper would benefit from highlighting the unique theoretical contributions more clearly. The differentiation from non-blind methods, especially in solving more general or harder inverse problems, should be emphasized to better showcase the method's potential and impact.\n\nIn summary, while the paper presents a novel and promising approach to image restoration using pretrained diffusion models, it would benefit from addressing the theoretical and clarity issues mentioned above. Strengthening these aspects will enhance the overall quality and impact of the work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see the detailed response below.\n\n### Q2. Specific areas needing attention\n\n>The phrase \"better neural network architecture choices\" on lines 21-22 should be made more specific to avoid ambiguity.\n\n\nthanks. We mean that better NN architectures (for example, Transformers) have led to better generative models. We will make this clearer in our revision.\n\n\n>Equations 1, 3, 4, 6, and 8: \\DeclareMathOperator*{\\argmin}{arg,min}\n\nthanks for pointing this out. We will correct all of them in our revision.\n\n> Lines 132-134: The wording and notation need clarification\n\nthanks. We will make the notation more clear.\n\n>The derivation of Eq. 8 seems out of place and might be better suited for section 3.2.3.\n\nthanks. We will move it to section 3.2.3.\n\n\n### Q3. introduction enhancement and [2, 3] should be discussed separately\n\nthanks for pointing this out. We will adjust the introduction and discuss [2, 3] in the related work.\n\n### Q4. Statement about GAN inversion methods on lines 104-105\n\nThanks for pointing this out. We will include the mentioned works in our revision.\n\n### Q5. Algorithm 1 and 2 are confusing with their indices.\n\nThanks for pointing this out. We will use clear indices for both Algorithm 1 and Algorithm 2 in our revision.\n\n\n### Q6. Solving more general IR tasks?\n\nBIRD can be applied to a wide range of IR tasks, not just the blind ones. BIRD can solve non-blind tasks (known degradation operators) like inpainting and colorization. We refer the reviewer to Figure 1 in our rebuttal PDF, where we show some visual results of our method solving more IR tasks. Our method remains the same as for the blind case, except that we do not optimize for the degradation operator (as it is known).\n\n### Q7. Solving IR tasks where the measurements are not in image space?\n\nYes, BIRD can handle IR tasks where the measurements are not in image space. Our method only requires a differentiable degradation operator (or some differentiable approximation of it). BIRD can handle the non-differentiable JPEG-deartifacting. In Figure 1, we show some visual results of the sparse-view CT.\n\n### Q8. The differentiation from non-blind methods, BIRD's potential and impact\n\nAlthough BIRD is primarily proposed as a blind zero-shot method, here we discuss some of the similarities/differences with non-blind methods. To further showcase the potential of BIRD, we highlight three aspects that demonstrate the advantages of our method.\n\n*Robustness to severe degradation*\n\nAs depicted in Figure 2 of our rebuttal PDF, BIRD is more robust to severe degradation (SRx16), both in terms of image quality and faithfulness.\n\n*Robustness to noise distribution*\n\nReal noise is usually not Gaussian. We compare BIRD with non-blind methods using a mixture of Gaussian and speckle noise.  As shown in Figure 3 of our rebuttal PDF, although DPS[2] is  robust to noise distribution, BIRD generates higher quality images.\n\n*Robustness to error in the degradation model*\n\nNon-blind methods generally rely on an off-the-shelf method to estimate the degradation operator. These off-the-shelf methods are not 100% accurate. Thus, a valuable feature of a non-blind IR method is its robustness to errors in degradation operator estimation. In Figure 4 of our rebuttal PDF, we show some visual results where we simulate a small error in the degradation operator. BIRD produces better quality outputs.\n\n\n|   **Method**|   **SR x16**| **SRx4  (noise with a mixture model)** |**Deblur (degradation operator with a small error)** |\n|---|---|---|---|\n|  DDNM[20] |  21.73/0.451 | 21.26/0.472  | n.a  | \n|  DPS[2] |  21.13/0.447 | 23.76/0.277  | 23.86 /0.360  | \n|  BIRD | 21.95/0.349  | 24.82/0.239  |  24.56/0.251  | \n\nQuantitative Comparison (PSNR/LPIPS) with state-of-the-art non-blind methods.\n\n### Q9. Problems causing the method to fail\n\nBIRD needs a parametric form of the degradation model (albeit with unknown parameters). Such a constraint is not satisfied for some IR problems like image deraining, and so our method cannot handle it. We mention this limitation in our main paper at lines (233-236).", "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": "Q4bOOlQLMn", "reviewer": "Reviewer_cmXb", "summary": "The paper introduces a blind image restoration method based on DDIM, which iteratively optimizes the initial noises and the degradation model parameters through the restoration loss of reconstructing the degraded image. As a result, the restored image remains on the data manifold of the pretrained diffusion model. The experiments on three image restoration tasks demonstrate the feasibility of the proposed method.", "questions": "Please address the concerns in the above Weaknesses.", "limitations": "Please see the above Weaknesses.", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The method do not alter the reverse sampling, and could generate images that lie on the data manifold of diffusion model at every iteration.\n2. The method is adaptable to multiple image restoration tasks, such as deblurring, super-resolution, and JPEG de-artifacting, without requiring model retraining or fine-tuning.", "weaknesses": "1. The inversion of generative models has been extensively used in both GAN and diffusion models. This work does not sufficiently distinguish itself from existing methods.\n2. The optimizable degradation model has been presented in the paper of GDP[1], and the iterative optimization of the degradation model and the restored image also has been adopted in the paper of TAO[2]. The authors have not adequately addressed how their method differs from these existing approaches.\n3. The paper claims that the method is computationally efficient, yet the timing results presented in Table 2 do not support this claim. In addition, despite the authors' assertion that their method achieves state-of-the-art results, the performance metrics in Table 4 do not substantiate this claim.\n[1] Fei B, Lyu Z, Pan L, et al. Generative diffusion prior for unified image restoration and enhancement[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 9935-9946.\n[2] Gou Y, Zhao H, Li B, et al. Test-Time Degradation Adaptation for Open-Set Image Restoration[C]//Forty-first International Conference on Machine Learning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see the detailed response below.\n\n\n### Q1. Further distinction from existing methods based on inversion\nFirst, we point that there is a a fundamental difference between *inverting a clean image* (mostly useful for applications like image editing), where we aim for the same image, and *inverting a degraded image* (useful for IR tasks), where we aim for the degradation-free image. Indeed, a lot of the literature related to the inversion of generative models applies to the clean case, which is different from what IR tasks aim to solve. Here, we further emphasize the key differences between BIRD and other IR methods based on diffusion and GAN  inversion.\n\n *Diffusion-based approaches*\n\nWe can fairly claim that BIRD is the *first* diffusion-based approach to invert a *degraded* image. By inversion, we mean obtaining the initial Gaussian noise $x_T$, which, when applied to the diffusion model, yields the clean image. There are a few methods that apply diffusion inversion to a clean image in the context of image editing, such as [3, 4]. Based on the assumption that the ODE process can be reversed in the limit of small steps, these methods run the diffusion in the reverse direction from $z_0$ to \\$z_T $ (from image space to Gaussian noise), rather than from $z_T$ to $ z_0$ to obtain the inverted latent. Unlike these methods, which solve a different task, BIRD is fundamentally different as it employs a gradient descent optimization approach, whereas [3, 4] do not. Moreover, applying those methods to a degraded image results in the same degraded image.\n\n\n*GAN-based approaches*\n\nThe IR methods based on GAN inversion can be mainly classified into two approaches: 1) learning-based methods such as [5, 6], which train an encoder to invert the GAN. These methods are clearly distinguishable from BIRD, as BIRD is not a learning-based method and does not involve training. 2) Optimization-based methods such as [7, 8]. Although both these methods and BIRD are gradient descent optimization methods, they differ in key ways: 1) They fine-tune the GAN or train an auxiliary network, whereas BIRD involves no fine-tuning or training. 2) A diffusion model differs from a GAN in aspects such as iterative sampling versus a single forward pass and inference speed. Simply applying a GAN-style inversion to a diffusion model would take on the order of hours, which is impractical.\n\nAlthough many methods apply GAN inversion to IR tasks, the literature still lacks a diffusion inversion method despite its potential advantages. We believe that BIRD fills this gap and brings all the benefits of diffusion combined with inversion. In our humble opinion, BIRD can open new perspectives on the applicability of diffusion models in IR tasks and encourage further exploration of diffusion inversion for IR applications.\n\n\n### Q2. Difference with GDP[1] and TAO[2], the iterative optimization of the degradation model and the restored image\n\nThe idea of jointly optimizing the degradation model and the clean image (or doing it iteratively) is not new and is neither a contribution of ours nor of GDP [1]. The contributions of GDP and BIRD specifically lie in *how* to use the diffusion prior to obtain the clean image. In this regard, BIRD is fundamentally different from all other methods, particularly from GDP [1]. As stated in our contributions (lines 65-67), BIRD is the *first* to frame the IR problem as a latent (initial noise) optimization problem within the context of diffusion models. Based on this fundamental difference, there are many algorithmic differences between GDP [1] and BIRD. For example, our method is a pure *optimization-based* approach, where we optimize a well-defined variable (the initial noise $z_T$ ), while GDP is a *sampling* method. Moreover, in GDP, the degradation model is updated after each diffusion step while in BIRD, it is updated only after the hole diffusion process.\n\nBIRD is also significantly different from TAO [2] because TAO is an open-set method, whereas BIRD is a zero-shot method. Additionally, BIRD focuses on diffusion inversion, while TAO [2] does not.\n\n\n###  Q3. Computational efficiency and state of the art?\n\nBIRD consistently yields the best quantitative results in Table 1 and Table 4, except in two cases. We believe that a state-of-the-art method does not necessarily outperform all other methods across all datasets and metrics. This is the case, for example, with GDP [2] and DPS [9]. Regarding computational efficiency, BIRD is slower than GDP but significantly better in terms of image quality. It is faster than the state-of-the-art BlindDPS while requiring five times less memory. We believe that BIRD presents the best trade-off between image quality and computational efficiency.\n\n\n[3] Prompt-to-Prompt Image Editing with Cross-Attention Control. arXiv 2022\n\n[4] Null-text Inversion for Editing Real Images using Guided Diffusion Models. CVPR 2024\n\n[5] High-fidelity image inpainting with gan inversion. ECCV 2022\n\n[6] Gan prior embedded network for blind face restoration in the wild. CVPR 2021\n\n[7] Robust unsupervised stylegan image restoration. CVPR 2023\n\n[8] Exploiting deep generative prior for versatile image restoration and manipulation. PAMI 2021\n\n[9] Diffusion Posterior Sampling for General Noisy Inverse Problems. ICLR 2023", "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:
We would like to thank all the reviewers for their time and feedback. We attached a pdf containing some additional results based on their comments and suggestions.

Meta-review: Scores 4 4 5 7

The paper proposes a new approach to blind image restoration using diffusion models.  Reviewer cmXb points out that the work is too close to existing methods, like GDP (Generative diffusion prior for unified image restoration and enhancement) and TAO (Test-Time Degradation Adaptation for Open-Set Image Restoration).  The rebuttal does clarify this.  Reviewer ebAr points out several problems in the presentation which the rebuttal again is able to address.  They also do provide some further theoretical analysis.  The concerns of reviewer PrQF were also reasonable addressed.  Overall the paper appears to be a solid contribution and can show with several experiments that their approach is better than other established reconstruction methods.  

The average score of the paper is 5.0.  However, the lower scoring reviewers didn't increase their score, after their concerns were (mostly) addressed.  In summary, I suggest to accept this paper (if space permits).
Decision: Accept (poster)