GeoNaviDiff: Transferring Disentangled Semantic Controls to Diffusion Features via Local Riemannian Navigation

Disentangled real-image manipulation requires factor-specific semantic control while preserving image fidelity and non-target content. StyleSpace $S$ provides interpretable controls but is limited by GAN inversion, whereas diffusion models offer stronger image realization without an explicit factorized control basis. We introduce GeoNaviDiff, an unsupervised cross-space framework that transfers disentangled StyleSpace interventions to local Riemannian trajectories in diffusion $h$-space. GeoNaviDiff constructs reconstruction-decoupled supervision by extracting a spherical Log-map tangent from a matched StyleGAN reconstruction-edit pair and parallel-transporting it to the real-image diffusion state. A shared, factor-conditioned Navigator predicts this tangent at inference, while norm-preserving geodesic realization and source-anchored rollout stabilize the reverse process without edited references or factor-specific models. Experiments across multiple datasets show that GeoNaviDiff outperforms the compared methods in fidelity, factor selectivity, edit locality, and trajectory smoothness.