This paper proposes a novel paradigm for facial privacy protection that unifies multiple characteristics including anonymity, diversity, reversibility and security within a single lightweight framework. We name it PRO-Face S, short for Privacy-preserving Reversible Obfuscation of Face images via Secure flow-based model. In the framework, an Invertible Neural Network (INN) is utilized to process the input image along with its pre-obfuscated form, and generate the privacy protected image that visually approximates to the pre-obfuscated one, thus ensuring privacy. The pre-obfuscation applied can be in diversified form with different strengths and styles specified by users. Along protection, a secret key is injected into the network such that the original image can only be recovered from the protection image via the same model given the correct key provided. Two modes of image recovery are devised to deal with malicious recovery attempts in different scenarios. Finally, extensive experiments conducted on three public image datasets demonstrate the superiority of the proposed framework over multiple state-of-the-art approaches.