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 \textbf{H}yperbolic \textbf{D}iffusion \textbf{R}ecommender \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 constructing a geometrically latent space grounded in hyperbolic geometry, incorporating interpretability measures to define the latent anisotropic diffusion processes. 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 restrict both radial and angular components to facilitate directional diffusion propagation, thereby ensuring the preservation of the original topological structure in user-item interaction graphs. Extensive experiments on three benchmark datasets demonstrate the effectiveness of HDRM. Our code is available at \url{https://anonymous.4open.science/status/HDRM-ECFA}.
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