Securing Internet of Things (IoT) devices presents increasing challenges due to their limited computational and energy resources. Radio Frequency Fingerprint Identification (RFFI) emerges as a promising authentication technique to identify wireless devices through hardware impairments. RFFI performance under low signal-to-noise ratio (SNR) scenarios is significantly degraded because the minute hardware features can be easily swamped in noise. In this paper, we leveraged the diffusion model to effectively restore the RFF under low SNR scenarios. Specifically, we trained a powerful noise predictor and tailored a noise removal algorithm to effectively reduce the noise level in the received signal and restore the device fingerprints. We used Wi-Fi as a case study and created a testbed involving 6 commercial off-the-shelf Wi-Fi dongles and a USRP N210 software-defined radio (SDR) platform. We conducted experimental evaluations on various SNR scenarios. The experimental results show that the proposed algorithm can improve the classification accuracy by up to 34.9%.