Abstract: Although diffusion models are rising as a powerful solution for blind face restoration, they are criticized for two problems: 1) slow training and inference speed, and 2) failure in preserving the original identity and fine-grained facial details. In this work, we propose WaveFace to solve the problems in the frequency domain, where low- and high-frequency components decomposed by wavelet transformation are considered individually to maximize authenticity as well as efficiency.The diffusion model is applied to recover the low-frequency component only, which presents general information of the original image but 1/16 in size. To preserve the original identity, the generation is conditioned on the low-frequency component of low-quality images at each denoising step. Meanwhile, high-frequency components at multiple decomposition levels are handled by an unified network, which recovers complex facial details in a single step. Evaluations on four benchmark datasets show that: 1) WaveFace outperforms state-of-the-art methods in the authenticity, especially in terms of identity preservation, and 2) authentic images are restored with the efficiency 10$\times$ faster than existing diffusion model-based BFR methods.