This paper proposes a novel and physically interpretable method for face editing based on arbitrary text prompts. Different from previous GAN-inversion-based face editing methods that manipulate the latent space of GANs, or diffusion-based methods that model image manipulation as a reverse diffusion process, we regard the face editing process as imposing vector flow fields on face images, representing the offset of spatial coordinates and color for each image pixel. Under the above-proposed paradigm, we represent the vector flow field in two ways: 1) explicitly represent the flow vectors with rasterized tensors, and 2) implicitly parameterize the flow vectors as continuous, smooth, and resolution-agnostic neural fields, by leveraging the recent advances of implicit neural representations. The flow vectors are iteratively optimized under the guidance of the pre-trained Contrastive Language-Image Pretraining~(CLIP) model by maximizing the correlation between the edited image and the text prompt. We also propose a learning-based one-shot face editing framework, which is fast and adaptable to any text prompt input. Our method can also be flexibly extended to real-time video face editing. Compared with state-of-the-art text-driven face editing methods, our method can generate physically interpretable face editing results with high identity consistency and image quality. Our code will be made publicly available.

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