# Blurring-Sharpening Process Models for Collaborative Filtering

arXiv: https://arxiv.org/abs/2211.09324 · HTML: https://mlsanity.com/paper/2211.09324/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 78 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 30 of 45)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)
- [Disentangled Graph Collaborative Filtering](https://mlsanity.com/paper/2007.01764/) (2020)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models](https://mlsanity.com/paper/1705.10513/) (2017)
- [Item2Vec: Neural Item Embedding for Collaborative Filtering](https://mlsanity.com/paper/1603.04259/) (2016)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)

## Built on by (most cited first, 30 of 35)

- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [AutoReproduce: Automatic AI Experiment Reproduction with Paper Lineage](https://mlsanity.com/paper/2505.20662/) (2025)
- [An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attention](https://mlsanity.com/paper/2312.10325/) (2023)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Score-based Generative Diffusion Models for Social Recommendations](https://mlsanity.com/paper/2412.15579/) (2024)
- [A Survey on Diffusion Models for Recommender Systems](https://mlsanity.com/paper/2409.05033/) (2024)
- [Collaborative Filtering Based on Diffusion Models: Unveiling the Potential of High-Order Connectivity](https://mlsanity.com/paper/2404.14240/) (2024)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [RecFusion: A Binomial Diffusion Process for 1D Data for Recommendation](https://mlsanity.com/paper/2306.08947/) (2023)
- [Turbo-CF: Matrix Decomposition-Free Graph Filtering for Fast Recommendation](https://mlsanity.com/paper/2404.14243/) (2024)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [Masked Diffusion for Generative Recommendation](https://mlsanity.com/paper/2511.23021/) (2025)
- [Differentially private and decentralized randomized power method](https://mlsanity.com/paper/2411.01931/) (2024)
- [S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain](https://mlsanity.com/paper/2501.00384/) (2024)
- [How Does Message Passing Improve Collaborative Filtering?](https://mlsanity.com/paper/2404.08660/) (2024)
- [SCONE: A Novel Stochastic Sampling to Generate Contrastive Views and Hard Negative Samples for Recommendation](https://mlsanity.com/paper/2405.00287/) (2024)
- [SVD-AE: Simple Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/2405.04746/) (2024)
- [RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2312.16563/) (2023)
- [Frequency-aware Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2402.08426/) (2024)
- [Exploring Feature-based Knowledge Distillation for Recommender System: A Frequency Perspective](https://mlsanity.com/paper/2411.10676/) (2024)
- [Diffusion Models in Recommendation Systems: A Survey](https://mlsanity.com/paper/2501.10548/) (2025)
- [Leveraging Member-Group Relations via Multi-View Graph Filtering for Effective Group Recommendation](https://mlsanity.com/paper/2502.09050/) (2025)
- [Continuous-time Discrete-space Diffusion Model for Recommendation](https://mlsanity.com/paper/2511.12114/) (2025)
- [QoS-Aware Graph Contrastive Learning for Web Service Recommendation](https://mlsanity.com/paper/2401.03162/) (2024)
- [Balancing User Preferences by Social Networks: A Condition-Guided Social Recommendation Model for Mitigating Popularity Bias](https://mlsanity.com/paper/2405.16772/) (2024)
- [Criteria-Aware Graph Filtering: Extremely Fast Yet Accurate Multi-Criteria Recommendation](https://mlsanity.com/paper/2502.09046/) (2025)
- [Towards Unified and Adaptive Cross-Domain Collaborative Filtering via Graph Signal Processing](https://mlsanity.com/paper/2407.12374/) (2024)
- [Diffusion-augmented Graph Contrastive Learning for Collaborative Filter](https://mlsanity.com/paper/2503.16290/) (2025)
- [LLM-Enhanced Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2508.13500/) (2025)

## Abstract (arXiv)

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.