Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This work proposed a novel zero-shot framework for linear image restoration, and the key module is denoising diffusion null-space model. It only requires a pretrained diffusion model, without further training and optimization. Experimental results show that the proposed method outperforms sota zero-shot restoration methods in many tasks.  
strength_and_weaknesses: Strength:
1.	This work proposes a unified theoretical framework for linear image restoration problems. Specifically, the sample x is decomposed into the range-space and null-space of A, which is the linear degradation operation. Then, the null-space is refined iteratively. 
2.	The proposed method can be utilized in many different tasks and the results are promising. 
Weaknesses:

1.	As demonstrated by the authors, DDNM+ can solve any real-world IR task as long as we we can construct an approximate linear degradation A and its pseudo-inverse A^-1. However, for real image degradation, A is most likely non-linear. For example, realistic noise in sRGB domain is nonlinear. If we directly utilize this method to solve real noise removal problem, I guess the performance will be heavily degraded. 

2.	The computing complexity. The authors should give the inference time to let readers aware of the computing complexity of the proposed method. 

clarity,_quality,_novelty_and_reproducibility: The contribution of this work is good since it constructs a general restoration model for arbitrary linear degradations. 
summary_of_the_review: Considering the novelty of this work and the good performance, I recommend accept.  

After rebuttal, the authors have addressed my concerns. Therefore, I still recommend accept.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a novel zero-shot framework for solving diverse linear image restoration (IR) problems, named Denoising Diffusion Null-Space Model (DDNM). Firstly, it provides detailed theory analysis for using a pre-trained diffusion model to solve linear IR problems. Secondly, the proposed DDNM can well solve those IR tasks with arbitrary degrees of degradation and also support solving noisy IR tasks.
strength_and_weaknesses: Strength: 

(1)This paper has detailed background introduction and theoretical analysis about using diffusion model to solve diverse IR problems. 

(2)This paper provides convincing proof and introduction about the usage of the generated null-space contents for image restoration.

(3)Another enhanced version DDNM+ is further proposed to handle noisy IR tasks. A time-travel trick is designed to provide better restoration quality.

(4)The provided quantitative and visual results validate the effectiveness of the proposed DDNM, which are superior over existing state-of-the-art zero-shot IR methods.

Weaknesses:

(1)The author mention the limitation of time efficiency in the appendix part. How about the memory efficiency?

(2)It is a little too absolute to claim that “solve arbitrary IR tasks with arbitrary degrees of degradation” in the introduction of contributions, since the degradation operators are asked to be linear.

clarity,_quality,_novelty_and_reproducibility: The clarity, quality and novelty of this paper is good. The reproducibility needs further improvement.
summary_of_the_review: In my opinion, this paper is marginally above the acceptance threshold based on the strengths and weaknesses.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The authors propose a novel method for zero-shot solution of image restoration problem formulated as linear inverse problems by modifying denoising diffusion models. In particular, they propose to only update the null space of the forward operator during the reverse process of the DDPM. Overall, the idea is novel, clearly explained and a significant amount of good experimental results on various problems is presented to support the work.
strength_and_weaknesses: Strengths:
- Interesting and novel idea to specialize the use of pretrained DDPMs for zero-shot solution of linear inverse problems
- Excellent experimental results on various tasks 

Weaknesses:
- It would be interesting to add a comparison of the proposed method with supervised discriminative models (e.g., SwinIR) trained for a specific restoration task to understand how far behind generative models are
- The authors acknowledge that computational complexity is a limitation of DDNM. However, they should also provide some experimental metrics such as the method runtime compared to existing methods
clarity,_quality,_novelty_and_reproducibility: The work is clearly explained and the idea is novel and sound. The explanation in section 3 seems to be self-contained enough to allow re-implementation of the method. The authors are highly encouraged to publicly release their original code.
summary_of_the_review: The paper presents a novel method based on DDPMs for zero-shot image restoration. The technique is novel and shows very competitive performance against other techniques based on generative models. The work is very valuable as an alternative to supervised training of discriminative models but a point of comparison between them should be included.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper proposed denoising diffusion probabilistic model for image restoration. They specially applied null-space projection at every iteration to target variable x and used A^T y as range spaced values. By considering only null-space contents in reverse process, they achieved realistic images with data consistency. They demonstrated several image restoration applications: super-resolution, inpainting, colorization
strength_and_weaknesses: They introduced null-space decomposition during reverse process in DDPM which helps to pursue robust data consistency and realistic image reconstruction. The detailed descriptions toward it are given in Algorithmic tables and associated illustration. It's easy to understand. Their supported results in Figure 3 and 4 are quite good qualities. The results seem to be beyond the bar of quality in ICLR.

However, I'm a bit afraid that the result seems to be far from original contents, which brings fake information such as figure 3 at 32x super-resolution on CelebA. It looks like a posterior sample not like a reconstruction results. In my opinion, 32x SR results can not be called as reconstruction, it's a synthetic image. DDNM provides 32x32 pixels out of 1pixel, and it's hard to avoid referring contents from synthetic textures of training manifold. Therefore, especially for face datasets, I couldn't accept it as recovered result. It is closer to synthesizing images irrelevant with ground-truth. Thus, I recommend the authors to provide residual images and ground-truth images  in super resolution example and other examples, too.
clarity,_quality,_novelty_and_reproducibility: In method section, authors provided clear description about their claims on Null space refining and summarized well in pseudo codes at Algorithm1 & 2. Except ablation study on effectiveness of Null space projection lacks. Comparisons with DDRM may be different from such ablation studies.

The quality of results is fine when we review result table 1 and supplementaries. However, I have some doubts on comparison with other supervised learning methods. Basically, their model, DDNM, is also necessary to see ground-truth set for training a generative model, so it would be similar situation with supervised learning setup: train on ground-truth set and then inference on unseen testset. Thus, it may be important to see comparisons with supervised learning baselines in result tables (currently, this paper is compared only with DDPM-based generative models.

In the perspective of novelty, this paper reminds me following paper,
Song, Yang, et al. "Solving inverse problems in medical imaging with score-based generative models." ICLR (2022).
This paper also introduced SDE for inverse problems and they use very much similar steps for sampling. Major difference from this work is the existence of null space projection of target x in reverse process. I'm convinced of the superiority of this manuscript upon the mentioned paper.

The paper contains detailed pseudo codes enough to be implemented, however, there is no actual source code and information for neural network's architectures.
summary_of_the_review: In general, this paper is well written and supported by remarkable results. The idea using null space component for residual components in reverse process in DDPM seems to be interesting. However, their approach is similar with the paper from ICLR 2022(above). Unless I see the performance difference with the ICLR 2022 paper or proper explanation of distinguishable points, I would be a doubt on effectiveness of null space projection. 

Also, I have a concern that reconstructions from severe conditions go beyond image restoration and become closer to arbitrary image synthesizing. To avoid such concerns, the results from supervised learning need to be demonstrated together.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper presents a novel zero-shot framework for linear image restoration, and the key component is a denoising diffusion null-space model. The framework only needs a pre-trained diffusion model, and doesn’t require further training and optimization. Experimental results show that the proposed method outperforms state-of-the-art zero-shot restoration methods in many tasks. The proposed framework in the paper is novel and interesting. Besides, the experiments are comprehensive and solid.  The review process is summarized as below: The paper eventually received a total of 4 positive reviews: 3 “Accept” and 1 “marginally above the acceptance” after the rebuttal. The rebuttal successfully addresses all the reviewers’ concerns, and all reviewers agree on accepting the paper. Authors provided additional experimental results to further strengthen the paper, and the revised version has been improved after taking into account all the comments and suggestions from reviewers. After reading the rebuttal and reviewers’ comments, the AC agrees with the reviewers and recommends accepting the paper because of its novelty, value, and solid experiments. 
justification_for_why_not_higher_score: This paper is a novel and solid application work for image restoration tasks. Considering that it is an application paper, and the potential impact might be limited, that is to say, the paper doesn't provide a fundamental contribution or make a breakthrough in the field, thus, the AC recommends "accept with spotlight". 
justification_for_why_not_lower_score: All 4 reviewers recommend accepting the paper, and 3 of them assign a score 8: "Accept".
Decision: Accept: notable-top-25%