FlowFace: Rectifying Identity Conditioning with Riemannian Geometry for Face Generation

Diffusion-based face generation commonly combines iden-tity cues and edit conditions through Euclidean mixing at the condi-tioning interface. This becomes fragile when facial attributes are cou-pled: naively adding feature vectors ignores their interactions and canlead to identity drift and artifacts. We present FlowFace, a geometry-aware identity-conditioning framework that rectifies the Stable Diffusionconditioning geometry during training without modifying the inferencesampler. FlowFace includes (i) a dual-stream manifold encoder inspiredby fiber bundles to disentangle geometry-related variation from seman-tic identity, (ii) a Lie-algebraic composition module based on a trun-cated BCH expansion to introduce an explicit interaction term betweencoupled edits, and (iii) a geodesic-consistency regularizer that learns alocal SPD metric that encourages Euclidean operations to better cor-relate with a geodesic-consistent surrogate under the learned geome-try. Experiments show that FlowFace outperforms strong baselines inidentity preservation, text alignment, and perceptual quality, while re-taining adapter-level inference efficiency. The code will be available athttps://github.com/SunFly0/Flowface.