With the advancement of face reconstruction (FR) systems, privacy-preserving face recognition (PPFR) has gained popularity for its secure face recognition, enhanced facial privacy protection, and robustness to various attacks. Besides, specific models and algorithms are proposed for face embedding protection by mapping embeddings to a secure space. However, there is a lack of studies on investigating and evaluating the possibility of extracting face images from embeddings of those systems, especially for PPFR. In this work, we introduce the first approach to exploit Kolmogorov-Arnold Network (KAN) for conducting embedding-to-face attacks against state-of-the-art (SOTA) FR and PPFR systems. Face embedding mapping (FEM) models are proposed to learn the distribution mapping relation between the embeddings from the initial domain and target domain. In comparison with Multi-Layer Perceptrons (MLP), we provide two variants, FEM-KAN and FEM-MLP, for efficient non-linear embedding-to-embedding mapping in order to reconstruct realistic face images from the corresponding face embedding. To verify our methods, we conduct extensive experiments with various PPFR and FR models. We also measure reconstructed face images with different metrics to evaluate the image quality. Through comprehensive experiments, we demonstrate the effectiveness of FEMs in accurate embedding mapping and face reconstruction.