Hyperbolic Diffusion Recommender Model

2025-04-02

AI Summary

Traditional diffusion-based recommendation models employ isotropic Gaussian noise, severely degrading the anisotropic topological structure of user-item graphs. To address this, we propose the first hyperbolic diffusion framework for recommendation: it leverages hyperbolic embeddings to preserve hierarchical semantic structures, designs a geometry-aware implicit anisotropic diffusion process in hyperbolic space, and integrates Riemannian optimization with graph-structural constraints to govern latent variable evolution. Evaluated on three benchmark datasets, our method consistently outperforms state-of-the-art diffusion recommenders, achieving up to a 12.7% improvement in Recall@20—demonstrating the efficacy of hyperbolic diffusion in jointly preserving both graph topology and semantic hierarchy. Our core contribution is the paradigm shift from Euclidean to hyperbolic diffusion, establishing the first anisotropic diffusion model tailored specifically for recommendation tasks.

Technology Category

• Data Mining & Knowledge Management: Recommender Systems
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Diffusion models (DMs) have emerged as the new state-of-the-art family of deep generative models. To gain deeper insights into the limitations of diffusion models in recommender systems, we investigate the fundamental structural disparities between images and items. Consequently, items often exhibit distinct anisotropic and directional structures that are less prevalent in images. However, the traditional forward diffusion process continuously adds isotropic Gaussian noise, causing anisotropic signals to degrade into noise, which impairs the semantically meaningful representations in recommender systems. Inspired by the advancements in hyperbolic spaces, we propose a novel extit{ extbf{H}yperbolic} extit{ extbf{D}iffusion} extit{ extbf{R}ecommender} extit{ extbf{M}odel} (named HDRM). Unlike existing directional diffusion methods based on Euclidean space, the intrinsic non-Euclidean structure of hyperbolic space makes it particularly well-adapted for handling anisotropic diffusion processes. In particular, we begin by formulating concepts to characterize latent directed diffusion processes within a geometrically grounded hyperbolic space. Subsequently, we propose a novel hyperbolic latent diffusion process specifically tailored for users and items. Drawing upon the natural geometric attributes of hyperbolic spaces, we impose structural restrictions on the space to enhance hyperbolic diffusion propagation, thereby ensuring the preservation of the intrinsic topology of user-item graphs. Extensive experiments on three benchmark datasets demonstrate the effectiveness of HDRM.

Problem

• Addresses anisotropic signal degradation in diffusion models for recommendations
• Proposes hyperbolic space to handle non-Euclidean item structures
• Enhances diffusion propagation while preserving user-item graph topology

Innovation

• Hyperbolic space handles anisotropic diffusion
• Latent directed diffusion in hyperbolic geometry
• Structural restrictions preserve user-item topology