Hyperbolic Diffusion Recommender Model

TL;DR

This work addresses diffusion-model limitations in recommender systems by exploiting hyperbolic geometry to preserve anisotropic item structures during diffusion. It introduces HDRM, a two-stage framework combining a hyperbolic geometric autoencoder with a hyperbolic latent diffusion process and geometry-aware structural restrictions. HDRM achieves consistent improvements over strong baselines across three real-world datasets, with ablations confirming the crucial roles of hyperbolic encoding, directional diffusion, and geometric constraints. The model's capacity to capture hierarchical, power-law-like user-item interactions suggests significant practical impact for robust, topology-preserving recommendations in sparse or structurally complex data.

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 \textit{\textbf{H}yperbolic} \textit{\textbf{D}iffusion} \textit{\textbf{R}ecommender} \textit{\textbf{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.

Figures (8)

• Figure 1: 2D visualization of the data using SVD decomposition, where each color corresponds to a unique category. (a) Euclidean visualization of the item features in MovieLens-1M; (b) Euclidean visualization of the image features in Fashion-MNIST; (c) Hyperbolic visualization of the item features in MovieLens-1M; (d) Hyperbolic visualization of the image features in Fashion-MNIST.
• Figure 2: An overview illustration of the HDRM architecture.
• Figure 3: The variation of model performance (R@10) across three datasets as diffusion steps and inference steps change.
• Figure 4: The variation of model performance across three datasets as the margin changes.
• Figure 5: The variation of model performance across three datasets as diffusion steps and inference steps change.