With the increasing availability of consumer depth sensors, 3D face recognition (FR) has attracted more and more attention. However, the data acquired by these sensors are often coarse and noisy, making them impractical to use directly. In this paper, we introduce an innovative Depth map denoising network (DMDNet) based on the Denoising Implicit Image Function (DIIF) to reduce noise and enhance the quality of facial depth images for low-quality 3D FR. After generating clean depth faces using DMDNet, we further design a powerful recognition network called Lightweight Depth and Normal Fusion network (LDNFNet), which incorporates a multi-branch fusion block to learn unique and complementary features between different modalities such as depth and normal images. Comprehensive experiments conducted on four distinct low-quality databases demonstrate the effectiveness and robustness of our proposed methods. Furthermore, when combining DMDNet and LDNFNet, we achieve state-of-the-art results on the Lock3DFace database.