  Collaborative filtering is one of the most fundamental topics for recommender
systems. Various methods have been proposed for collaborative filtering,
ranging from matrix factorization to graph convolutional methods. Being
inspired by recent successes of graph filtering-based methods and score-based
generative models (SGMs), we present a novel concept of blurring-sharpening
process model (BSPM). SGMs and BSPMs share the same processing philosophy that
new information can be discovered (e.g., new images are generated in the case
of SGMs) while original information is first perturbed and then recovered to
its original form. However, SGMs and our BSPMs deal with different types of
information, and their optimal perturbation and recovery processes have
fundamental discrepancies. Therefore, our BSPMs have different forms from SGMs.
In addition, our concept not only theoretically subsumes many existing
collaborative filtering models but also outperforms them in terms of Recall and
NDCG in the three benchmark datasets, Gowalla, Yelp2018, and Amazon-book. In
addition, the processing time of our method is comparable to other fast
baselines. Our proposed concept has much potential in the future to be enhanced
by designing better blurring (i.e., perturbation) and sharpening (i.e.,
recovery) processes than what we use in this paper.
