RGB-to-hyperspectral image reconstruction is a highly ill-posed inverse problem, since multiple plausible spectral distributions may correspond to the same RGB observation. Existing regression-based methods usually learn a deterministic mapping, which limits their ability to model reconstruction uncertainty and often leads to over-smoothed spectral responses. Although diffusion models provide strong distribution modeling capability, their direct application to hyperspectral reconstruction remains challenging due to the high spectral dimensionality, strong inter-band correlations, and strict requirement for spectral fidelity. To this end, we propose R2H-Diff, an efficient diffusion-based framework tailored for RGB-to-HSI reconstruction. Specifically, R2H-Diff formulates spectral recovery as a conditional iterative refinement process, enabling progressive reconstruction under RGB guidance. We proposed a Guided Spectral Refinement Module for RGB-conditioned feature fusion and a Hyperspectral-Adaptive Transposed Attention module for efficient spatial--spectral dependency modeling. Furthermore, a normalization-free denoising backbone is adopted to preserve spectral amplitude consistency, while a task-adapted linear noise schedule enables high-quality reconstruction with only five denoising steps. Extensive experiments on NTIRE2022, CAVE, and Harvard demonstrate that R2H-Diff achieves a favorable balance between reconstruction quality and computational efficiency. Notably, on NTIRE2022, R2H-Diff obtains 35.37 dB PSNR with a sub-million-parameter model of 0.58M parameters and 12.25G FLOPs, achieving the lowest model complexity among the evaluated methods while maintaining strong reconstruction fidelity.