Graph Signal Diffusion Model for Collaborative Filtering

TL;DR

This work addresses the limitation of standard diffusion models for collaborative filtering by introducing GiffCF, a Graph Signal Diffusion Model that operates on an item-item similarity graph using a heat-equation-inspired forward process. The forward diffusion applies graph smoothing via a family of filters to inject graph structure as prior knowledge, while the reverse process uses a two-stage, history-conditioned denoiser in a deterministic sampling scheme to reconstruct high-quality interaction vectors. GiffCF demonstrates state-of-the-art performance on three large benchmarks, with extensive analyses showing the importance of the forward graph design, the refining-sharpening reverse steps, and the denoiser architecture. The approach highlights the potential of combining diffusion modeling with graph signal processing for scalable, structure-aware recommender systems, and suggests directions for more powerful denoisers and additional conditioning signals.

Abstract

Collaborative filtering is a critical technique in recommender systems. It has been increasingly viewed as a conditional generative task for user feedback data, where newly developed diffusion model shows great potential. However, existing studies on diffusion model lack effective solutions for modeling implicit feedback. Particularly, the standard isotropic diffusion process overlooks correlation between items, misaligned with the graphical structure of the interaction space. Meanwhile, Gaussian noise destroys personalized information in a user's interaction vector, causing difficulty in its reconstruction. In this paper, we adapt standard diffusion model and propose a novel Graph Signal Diffusion Model for Collaborative Filtering (named GiffCF). To better represent the correlated distribution of user-item interactions, we define a generalized diffusion process using heat equation on the item-item similarity graph. Our forward process smooths interaction signals with an advanced family of graph filters, introducing the graph adjacency as beneficial prior knowledge for recommendation. Our reverse process iteratively refines and sharpens latent signals in a noise-free manner, where the updates are conditioned on the user's history and computed from a carefully designed two-stage denoiser, leading to high-quality reconstruction. 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.

Figures (8)

• Figure 1: Comparison of different diffusion processes for implicit feedback. Standard Gaussian diffusion destroys personalized information in the interaction matrix with Gaussian noise. On the contrary, our graph signal diffusion corrupts interaction signals into smoothed preference signals, leveraging the graphical structure of the interaction space. Each square in (a) represents a matrix entry, and each circle in (b) represents a scalar-valued graph node. Deeper colors indicate higher values.
• Figure 2: Graphical models for different recommender models at inference time. Latent variables are colored in blue.
• Figure 3: The architecture of the denoiser $\hat{{\bm{x}}}_\theta$ in GiffCF.
• Figure 4: Effect of the number of diffusion steps $T$.
• Figure 5: Effect of the smoothing strength $\alpha$.