## Reviewer 1 **Overall evaluation:** -2 (reject) ### Overall evaluation (comments) I suggest rejecting this submission for following reasons: 1. The proposed method is claimed to be able to skip the training process of embedding vectors, while the singular vectors of \tilde{R} are still required with the equivalent computational cost. 2.I would expect the experimental result on the large dataset, instead of the dataset with large sparsity. It is hard to imagine this work's contribution to the industry without solid number. ### Strengths and reasons to accept 1. The method is straightforward (perturbation and recovery) and easy to follow. ### Weaknesses and limitations 1. In the ablation study, it is unclear how to set up the correct model structure with respect to the residual connection. It is not clear why the residual connection improves the performance on one dataset instead of the others. 2. In Eq. (10), the graph convolution process only considers the 1-step away neighborhood, while it ignores that multiple steps neighborhoods may have a significant effect on the low-pass filter. ## Reviewer 2 **Overall evaluation:** 1 (weak accept) ### Overall evaluation (comments) This paper is somewhat interesting as it studies collaborative filtering by Blurring-Sharpening process models. It seems that this is the first study in this regard. The proposed model does not need training ans exhibit good performanced compared to many recent models. ### Strengths and reasons to accept (1) This paper is the first study that proposes the blurring-sharpening process paradigm for collaborative filtering/ (2) The proposed method does not need training. And as shown in Table 6, this method is very efficient in the training stage. (3) Many different baselines are adopted for comparing with the proposed model. ### Weaknesses and limitations (1) The motivation of why using Blurring-Sharpening process is not introduced in Sec. 1. In the current version, it looks like there is no existing studies in this regard, so this study tries this technique for recommendation. (2) Some key details about the proposed approach is unclear. For example, how to solve Eq. 15 and 16 is not presented. The reason why b_{GF-CF} has the form in Blurring process is not introduced as well. (3) This method seems good at dealing with batch data, but when used for deployment, it is not convenient for generating recommendation for one user each time. This is also reflected by the inference time reported in Table 7. ## Reviewer 3 **Overall evaluation:** 1 (weak accept) ### Overall evaluation (comments) In this paper, the authors propose a novel paradigm of Blurring-Sharpening Process Model (BSPM) for collaborative filtering. The proposed blurring and sharpening processes are formulated as differential equations. They also show that some of the existing graph convolution-based collaborative filtering methods are special cases of the proposed model. ### Strengths and reasons to accept 1. design a perturbation-recovery concept, called the Blurring-Sharpening Process Model (BSPM), for collaborative filtering. 2. the BSPM directly perturbs (blurs) the user-item interaction matrix, and recovers (sharpens) the blurred matrix to derive unknown user-item interactions. 3. The experimental results are pretty good, comparing the SOAT baseline. ### Weaknesses and limitations 1. The code is not release, the reproducibility is unclear. 2. The inference time is much larger than the baselines based on Table 7. It is good that the proposed model has very excitng training time, but with much more inference time. In real-world deployment. People care more about inference time since the training can be performed offline. ## Meta-review ### Meta-review The authors propose a blurring-sharpening approach for collaborative filtering inspired by recent advances in diffusion models. The reviewers appreciate the relevance and timeliness of the problem as well as the novelty of the proposed approach. On the other hand, a few key technical details are unclear, which limits the reproducibility of the approach. Moreover, despite a faster training time, the incurred overhead of the approach at inference time also raised concerns regarding its potential applicability in a real deployment.