Title: Blind Image Restoration via Fast Diffusion Inversion
Venue: NeurIPS 2024
Accepted: yes
Keywords: blind image restoration

diffusion models

unsupervised learning
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

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. Project page: https://hamadichihaoui.github.io/BIRD .

1 Introduction

Recent advances in generative learning due to the development of diffusion models [7, 18] have led to models capable of 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 diffusion 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 to 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). We call this method BIRD, which stands for Blind Image Restoration via fast Diffusion inversion. Since BIRD does not need to pre-train a model for the degradation operator, it can be used immediately on a wide range of IR tasks such as Gaussian deblurring, motion deblurring, super-resolution and denoising (see Figure 2). In this work, we show that having a strong image prior and ensuring that the restored image never leaves the data manifold during the reconstruction process are fundamental properties to generalize to a wide range of image degradation 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

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

though we have a 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 (l)) than the final image estimate from BlindDPS (see (e) top), which uses a quite accurate blur kernel estimate (see (e) bottom). This speaks of the importance of defining a strong image prior first and foremost.

BIRD is the first to cast an IR task as a 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;

BIRD is computationally efficient; we propose a fast diffusion model inversion in the context of image restoration, without fine-tuning nor retraining;

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 is 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 a 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-blind methods are [3] and DPS [2]. [3] points out that relying on an iterative procedure consisting of reverse diffusion steps and a projection-based consistency step runs the risk of stepping outside of the data manifold, a 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 a zero-shot framework for

Motion Deblur

Denoising

4

×

SR

IR tasks based on 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-based method. BlindDPS proposes an extension of [2] to 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 a model for each new degradation operator can be time-consuming. Fast Diffusion EM [9] proposes a method for blind image deblurring. It applies the Expectation-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 a Gibbs sampler to enable efficient sampling from the posterior distribution. In contrast to these works, in BIRD we introduce a blind image restoration method based on a novel diffusion inversion for DDIM. Our method is computationally efficient, as it requires only a few reverse diffusion steps, and generates realistic samples by only estimating the initial noise.

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, a number of methods [14, 15, 22, 23] inverts pre-trained GANs to solve image restoration problems. DGPGAN [14] performs the GAN inversion on a 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 an encoder to invert a pre-trained GANs on a

(a)

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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 on 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 fine-tuned/trained.

3 Image Restoration via BIRD

In this section, we introduce the classic Bayesian formulation of inverse problems applied to a 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 a Posteriori (MAP) optimization problem [24]

where ˆ x ∈ R N x × M x is the restored image of size N x × M x pixels, y ∈ R N y × M y is the degraded image of size N y × M y pixels, where p ( y | x ) is the so-called likelihood and p ( x ) the prior distribution. Inverse problems describe IR tasks with a degradation operator H η : R N x × M x → R N y × M y and a noise image n ∈ R N y × M y , such that the observed degraded image y can be written as

η is a vector with all the parameters that define the operator H η . IR tasks such as image denoising, deblurring and super-resolution can all be described using specific choices of H η . For instance, in the case of image deblurring, the H η operator can be described as a convolution with a blur kernel k such that H η ( x ) . = k ∗ x , where ∗ denotes the convolution operation. In the blind deblurring problem, one assumes that H η takes the form of a convolution, but without knowing its parameters η , which, in this case, are the values of the true blur kernel k . Thus, we also need to estimate the parameters η as part of the optimization procedure. Only in the special case of image denoising we do use H η as the identity function. By assuming that the noise n is zero mean Gaussian in the MAP formulation, one can rewrite eq. (1) as

where R ( x ) is also called a regularization term, and λ > 0 is a coefficient that regulates the interplay between the likelihood and the prior. We define Ω x ∈ R N x × M x as the (compact) set of degradationfree (realistic) images and we propose employing a formulation that implicitly assumes a uniform

Algorithm 1 BIRD: Image Restoration

Require: Degraded image y , step size δt , the dimension of x d = N x M x , learning rate α , the stop threshold ε

Ensure:

Return ˆ x 0

1: Initialize x 0 T ∼ N (0 , I ) and H η 0 with random parameters

2: while k : 1 → N and L IR ( x k 0 , H η k ) > ε do

3: x k 0 = DDIMReverse ( x k T , δt )

4: x k +1 T = x k T - α ∇ x T L IR ( x k 0 , H η k )

5: x k +1 T = x k +1 T ∥ x k +1 T ∥ √ d

6: η k +1 = η k - α ∇ η L IR ( x k 0 , H η k )

7: end while

8: return ˆ x 0 = DDIMReverse ( x N T , δt )

Algorithm 2 DDIMReverse ( x T , δt )

Require: : Initial noise x T ∼ N (0 , I ) , step size δt

1: t = T

2: while t > 0 do

3: ˆ x 0 | t = ( x t - √ 1 - ¯ α t ϵ θ ( x t , t )) / √ ¯ α t

4: x t - δt = √ ¯ α t - δt ˆ x 0 | t + √ 1 - ¯ α t - δt . x t - √ ¯ α t ˆ x 0 | t √ 1 - ¯ α t

5: t ← t - δt

6: end while

7: return ˆ x 0

prior p ( x ) . = p U ( x ) on Ω x . That is, R ( x ) = -log( p U ( x )) = -log( c · 1 Ω x ( x )) , where c is a normalizing constant and 1 Ω x ( x ) is 1 if x is in the support of Ω x and 0 otherwise.

This results in the following simplified formulation

To ensure that x ∈ Ω x , we parameterize x via the initial noise z of a pre-trained diffusion model g : R N x × M x → R N x × M x trained by mapping noise samples from the high-density region of the standard Normal distribution (that we denote Ω z ) to the domain of degradation-free (realistic) images Ω x . In other words, we assume that Ω x = { g ( z ) } ∣ ∣ z ∈ Ω z . The optimization objective eq. (4) becomes then

with ˆ x = g (ˆ z ) . In high dimensions, 1 N x M x ∥ z ∥ 2 ≈ E [ zz ⊤ ] = variance ( z ) = 1 as N x M x ↦→∞ . In fact, most of the density of a high-dimensional Normal random variable is around ∥ z ∥ 2 = N x M x [12, 20]. Therefore, we propose to approximate the original problem (3) with

3.2 An Efficient Diffusion Inversion

In problem (6), we implement the function g by adopting a pre-trained diffusion model. We choose the Denoising Diffusion Implicit Model (DDIM) [17] and set it as a fully deterministic diffusion process. To solve problem (6), we propose an optimization-based iterative procedure. We jointly estimate a realistic image x ( i . e ., with a high p ( x ) ) and the forward degradation model H η such that H η ( x ) ≈ y . In order to find x , we explicitly exploit the correspondence between image samples x and their associated initial latent image z in DDIMs, in contrast to the mappings used in prior work [8, 11, 21]. Thus, we aim to find the initial noise sample z that can generate the image x when applied to DDIM. To keep the notation consistent with the DDIM formalism, we denote images x with x 0 and the samples z with x T , where T is the number of iterations in the diffusion model. To make our presentation self-contained, we briefly revise the notation and notions of diffusion models.

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 on a stochastic iterative denoising process or by learning the explicit dynamics of the reverse process, e . g ., through an ODE [17]. More precisely the forward diffusion process maps an image x 0 ∼ p ( x ) to a zero-mean Gaussian x T ∼ N (0 , I ) by generating intermediate images x t for t ∈ [1 , T ] which are progressively noisier versions of x 0 . DDPM [7] adopts a Markovian diffusion process, where x t only depends on x t -1 . Given a non-increasing sequence α 1: T ∈ (0 , 1] , the joint and marginal distributions of the forward diffusion process are described by

which implies that we can sample x t simply by conditioning on x 0 with ¯ α t = ∏ s ≤ t α s via

To invert the forward process, one can train a model ϵ θ , with parameters θ , to minimize the objective

Given the initial noise x T , image samples x 0 are obtained by iterating for t ∈ [1 , T ] the denoising update

with z ∼ N (0 , I ) , and σ 2 t = 1 -¯ α t -1 1 -¯ α t (1 -α t ) .

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 eq. (10) becomes computationally expensive. To reduce the computational cost, they propose to use instead

a Denoising Diffusion Implicit Model (DDIM) [17], which foregoes the Markovian assumption in favor of a diffusion process where q ( x T | x 0 ) = N ( √ ¯ α T x 0 , (1 -¯ α T ) I ) and

LR

GDP [6]

BlindDPS [1]

BIRD

GT

When σ t = 0 for all t , the diffusion process is fully deterministic . This means that when we start from the same noise sample x T we obtain the same generated image sample. Given x t , one can first predict the denoised observation ˆ x 0 , which is a prediction of x 0 given x t

Then, we can predict x t -1 from x t and ˆ x 0 using eq. (12) by setting σ t = 0

with ˆ ω = x t - √ ¯ α t ˆ x 0 √ 1 -¯ α t a direction pointing to x t . [17] shows that this formulation allows DDIM to use fewer time steps at inference by directly predicting x t -τ with τ > 1 , which results in a more computationally efficient process using

3.2.2 Accelerated DDIM Sampling

As previously mentioned, we adopt DDIMs as 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 x T ∼ N (0 , I ) . Instead of denoising x T iteratively for all the steps used in the pre-training, we make larger steps by using intermediate estimates of ˆ x 0 | t from x t using the pre-trained DDIM model ϵ θ via

We define the hyper-parameter δt that controls the number of denoising steps, and we can directly jump to estimate x t -δt from ˆ x 0 | t and x t using

A larger step size δt allows us to favor speed, while a lower one favors precision or fidelity. This iterative procedure, which we summarize in Algorithm 2, results in an estimate of x 0 that is differentiable in x T . We denote by DDIMReverse ( ., δt ) the mapping function between x T and x 0 that is parameterized with the step size δt (this is essentially our choice of g in problem (6)). Figure 3 shows sampled images x 0 using different δt starting from the same initial noise x T through DDIMReverse ( ., δt ) .

GDP [6]

BlindDPS [1]

BIRD

GT

Noisy

DIP [19]

BIRD

GT

VE

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 a superscript to the estimated unknowns. It starts from an initial noise instance x 0 T ∼ N (0 , I ) and a parametric degradation model H η 0 , where η 0 is randomly initialized. At each iteration k , we first compute our estimate of the clean image x k 0 by mapping x k T through DDIMReverse ( ., δt )

We then compute the restoration loss

Given an initial noise x k T and H η k , the optimization iteration is simply derived through gradient descent with a learning rate α

To impose the normalization constraint on x T we set its Euclidean norm to ∥ x T ∥ = √ N x M x via

After N iterations, or when L IR ( x N 0 , H η N ) becomes small enough, we deem that BIRD has converged. The restored image ˆ x 0 is then generated by ˆ x 0 = DDIMReverse ( x N T , δt ) , which always ensures that ˆ x 0 is within the manifold of realistic images, as already shown in Figure 3. Moreover, in Figure 4 we show two examples of the reconstruction with H η ( x ) = x and with y un-corrupted noise-free images from the validation dataset of ImageNet [5] and CelebA [10]. We summarize this iterative procedure in Algorithm 1.

4 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, we use an anisotropic Gaussian

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 a noise standard deviation of σ ≈ 0 . 05 . For image denoising, we introduce a combination of Gaussian (signal-independent) and speckle (signal-dependent) noises simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. For all our experiments, we use δt = 100 and a maximum number of iterations N = 200 . Adam is adopted as an optimizer with a 0 . 003 learning rate. We evaluate our method both on the validation datasets of ImageNet [5] and CelebA [10] at 256 × 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, 7 show non cherry-picked examples of ImageNet and CelebA images restored in the cases of 4 × 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 2 report the performance of BIRD as well as 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 art 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 δt . All experiments are carried out on a GeForce GTX 1080 Ti.

Effect of the step size δt : The step size δt defines a trade-off between speed and accuracy. Table 3 shows the PSNR, LPIPS and runtime for image denoising on CelebA. We observe that the reconstruction accuracy of BIRD is not too sensitive to this parameter, while the runtime is linearly affected. δt = 100 gives a 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 a Naive Inversion , which performs the inversion by unrolling all the steps of the pre-trained diffusion model. This case

shows how BIRD results in a significantly faster execution. Despite being an iterative method, BIRD has a reasonable runtime making it a practical IR method. The reported speed uses δt = 100 .

4.5 Limitations and Broader Impacts

We have evaluated our method on degradation operators with a 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-induced biases.

5 Conclusion

We have introduced BIRD, a 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 in DDIM by casting the inverse restoration problem as a latent estimation problem. Our framework does not require training networks on specific task, but can instead be directly applied to 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 on blind image restoration tasks including Gaussian deblurring, motion deblurring, super-resolution and denoising.

Acknoweledgements. We acknowledge the support of the SNF project number 200020_200304.

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Clean target

not available.

A Appendix / supplemental material

A.1 Application of BIRD to non-blind cases

Naturally, BIRD can also be applied to 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 sparse-view CT image reconstruction.

A.2 Robustness of BIRD to 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 ( × 16 super-resolution). BIRD outperforms the other methods in 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 on off-the-shelf methods to estimate the degradation operator. These off-the-shelf methods are not 100% accurate. We simulate a small error in the degradation operator and we use the simulated kernel (plus this error) to generate the restored image for the non-blind DPS [2] and BIRD. As shown in Figure 10, BIRD produces better quality outputs compared to the non-blind method DPS when using the kernel with a slightly simulated error.

LR

DDNM

DPS

BIRD

GT

ITISHA

ART

FILMAN

Angeles

(a)

DPS

BIRD (ours)

GT

NeurIPS Paper Checklist

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes]

Justification: We claim that defining an image prior such that restored images during the iterative process are realistic is fundamental to have a robust and accurate IR method. Our experiments on several IR tasks support this claim.

Guidelines:

The answer NA means that the abstract and introduction do not include the claims made in the paper.

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.

The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.

It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes]

Justification: See at the end of the Experiments section.

Guidelines:

The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS:\n1. 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.\n\nWEAKNESSES:\n1. 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.\n\nQUESTIONS:\nPlease address the concerns in the above Weaknesses.\n\nLIMITATIONS:\nPlease see the above Weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS:\nThis 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.\n\nWEAKNESSES:\nThe 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.\n\nQUESTIONS:\nHow does the method work for general inverse problems? Does Algorithm 1 actually require the measurements to be in image space?\n\nLIMITATIONS:\n- 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS:\nThe idea of diffusion inversion is interesting and reasonable, which broaden the concept of deep generative prior, and can possibly motivated more related studies.\n\nWEAKNESSES:\nThe 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.\n\nQUESTIONS:\nIt seems that Figure 1 indeed shows an example of deblurring with motion blur, while the caption says Gaussian blur.\n\nLIMITATIONS:\nThe authors have discussed the limitations, which are reasonable.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS:\n- 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.\n\nWEAKNESSES:\n- 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.\n\nQUESTIONS:\n- 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).\n\nLIMITATIONS:\nno comments.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-15"}