Reconfigurable intelligent surface (RIS) has been recognized as a promising technology for next-generation wireless communications. However, the performance of RIS-assisted systems critically depends on accurate channel state information (CSI). To address this challenge, this letter proposes a novel channel estimation method for RIS-aided millimeter-wave (mmWave) systems based on diffusion models (DMs). Specifically, the forward diffusion process of the original signal is formulated to model the received signal as a noisy observation within the framework of DMs. Subsequently, the channel estimation task is formulated as the reverse diffusion process, and a sampling algorithm based on denoising diffusion implicit models (DDIMs) is developed to enable effective inference. Furthermore, a lightweight neural network, termed BRCNet, is introduced to replace the conventional U-Net, significantly reducing the number of parameters and computational complexity. Extensive experiments conducted under various scenarios demonstrate that the proposed method consistently outperforms existing baselines.