Generative design of functional RNAs presents revolutionary opportunities for diverse RNA-based biotechnologies and biomedical applications. To this end, RNA inverse folding is a promising strategy for generatively designing new RNA sequences that can fold into desired topological structures. However, three-dimensional (3D) RNA inverse folding remains highly challenging due to limited availability of experimentally derived 3D structural data and unique characteristics of RNA 3D structures. In this study, we propose RIdiffusion, a hyperbolic denoising diffusion generative RNA inverse folding model, for 3D RNA design tasks. By embedding geometric features of RNA 3D structures and topological properties into hyperbolic space, RIdiffusion efficiently recovers the distribution of nucleotides for targeted RNA 3D structures based on limited training samples using a discrete diffusion model. We perform extensive evaluations on RIdiffusion using different data sets and strict data-splitting strategies and the results demonstrate that RIdiffusion consistently outperforms baseline generative models for RNA inverse folding. This study introduces RIdiffusion as a powerful tool for the generative design of functional RNAs, even in structure-data-scarce scenarios. By leveraging geometric deep learning, RIdiffusion enhances performance and holds promise for diverse downstream applications.