Current face de-identification methods that replace identifiable cues in the face region with other sacrifices utilities contributing to realism, such as age and gender. To retrieve the damaged realism, we present FLUID (Face de-identification in the Latent space via Utility-preserving Identity Displacement), a single-input face de-identification framework that directly replaces identity features in the latent space of a pretrained diffusion model without affecting the model's weights. We reinterpret face de-identification as an image editing task in the latent h-space of a pretrained unconditional diffusion model. Our framework estimates identity-editing directions through optimization guided by loss functions that encourage attribute preservation while suppressing identity signals. We further introduce both linear and geodesic (tangent-based) editing schemes to effectively navigate the latent manifold. Experiments on CelebA-HQ and FFHQ show that FLUID achieves a superior balance between identity suppression and attribute preservation, outperforming existing de-identification approaches in both qualitative and quantitative evaluations.