Collaborative filtering is a critical technique in recommender systems. Among various methods, an increasingly popular paradigm is to reconstruct user-item interactions based on the historical observations. This can be viewed as a conditional generative task, where recently developed diffusion model demonstrates great potential. However, existing studies on diffusion models lack effective solutions for modeling implicit feedback data. Particularly, the isotropic nature of the standard diffusion process fails to account for the heterogeneous dependencies among items, leading to a misalignment with the graphical structure of the interaction space. Meanwhile, random noise destroying personalized information in interaction vectors, causing difficulty in reverse reconstruction. In this paper, we make novel adaptions of diffusion model and propose Graph Signal Diffusion Model for Collaborative Filtering (named GiffCF). To better represent the high-dimensional and sparse distribution of implicit feedback, we define a generalized form of denoising diffusion using heat equation on the item-item similarity graph. Our forward process smooths interaction signals with an advanced family of graph filters. Hence, instead of losing information, it involves item-item similarities as beneficial prior knowledge for recommendation. To reconstruct high-quality interactions, our reverse process iteratively refines and sharpens preference signals in a deterministic manner, where the update direction is conditioned on the user history and computed from a carefully designed two-stage denoiser. Finally, through extensive experiments, we show that GiffCF effectively leverages the advantages of both diffusion model and graph signal processing, and achieves state-of-the-art performance on three benchmark datasets.

翻译：协同过滤是推荐系统中的关键技术。在众多方法中，一种日益流行的范式是基于历史观测重建用户-项目交互。这可以视为条件生成任务，而近期发展的扩散模型在其中展现出巨大潜力。然而，现有扩散模型研究缺乏针对隐式反馈数据建模的有效方案。具体而言，标准扩散过程的各向同性特性未能考虑项目间的异质依赖关系，导致其与交互空间的图结构存在偏差。同时，随机噪声会破坏交互向量中的个性化信息，造成逆向重建困难。本文对扩散模型进行创新性改编，提出面向协同过滤的图信号扩散模型（命名为GiffCF）。为更好表征隐式反馈的高维稀疏分布，我们利用项目-项目相似度图上的热方程定义了去噪扩散的广义形式。其中，前向过程通过先进的图滤波器族平滑交互信号，从而在保留信息的同时引入项目间相似性作为有益的推荐先验知识。为重建高质量交互，逆向过程以确定性方式迭代优化和锐化偏好信号，其更新方向基于用户历史条件，并由精心设计的两阶段去噪器计算得出。最后，通过大量实验证明，GiffCF有效融合了扩散模型与图信号处理的双重优势，在三个基准数据集上达到了最先进性能。