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.

翻译：扩散模型已成为新一代最先进的深度生成模型。为深入理解扩散模型在推荐系统中的局限性，我们研究了图像与物品之间根本的结构差异。因此，物品通常表现出独特的各向异性和方向性结构，而这些结构在图像中较少出现。然而，传统的前向扩散过程持续添加各向同性的高斯噪声，导致各向异性信号退化为噪声，从而损害了推荐系统中具有语义意义的表征。受双曲空间研究进展的启发，我们提出了一种新颖的**双曲扩散推荐模型**（命名为HDRM）。与现有基于欧几里得空间的定向扩散方法不同，双曲空间固有的非欧几里得结构使其特别适合处理各向异性扩散过程。具体而言，我们首先在几何基础的双曲空间内构建概念以表征潜在的定向扩散过程。随后，我们提出了一种专门为用户和物品定制的新型双曲潜在扩散过程。基于双曲空间固有的几何属性，我们对空间施加结构约束以增强双曲扩散传播，从而确保用户-物品图的内在拓扑结构得以保留。在三个基准数据集上的大量实验证明了HDRM的有效性。