High-fidelity kinship face synthesis has many potential applications, such as kinship verification, missing child identification, and social media analysis. However, it is challenging to synthesize high-quality descendant faces with genetic relations due to the lack of large-scale, high-quality annotated kinship data. This paper proposes RFG (Region-level Facial Gene) extraction framework to address this issue. We propose to use IGE (Image-based Gene Encoder), LGE (Latent-based Gene Encoder) and Gene Decoder to learn the RFGs of a given face image, and the relationships between RFGs and the latent space of StyleGAN2. As cycle-like losses are designed to measure the L_2 distances between the output of Gene Decoder and image encoder, and that between the output of LGE and IGE, only face images are required to train our framework, i.e. no paired kinship face data is required. Based upon the proposed RFGs, a crossover and mutation module is further designed to inherit the facial parts of parents. A Gene Pool has also been used to introduce the variations into the mutation of RFGs. The diversity of the faces of descendants can thus be significantly increased. Qualitative, quantitative, and subjective experiments on FIW, TSKinFace, and FF-Databases clearly show that the quality and diversity of kinship faces generated by our approach are much better than the existing state-of-the-art methods.