Dragometry: 3D Geometric Control for Drag-Based Facial Image Editing

Point-based drag editing provides an intuitive interface for image manipulation, but existing diffusion-based methods typically operate on learned intermediate representations in which geometric information is encoded only implicitly. Geometry-conditioned diffusion models offer a different setting: explicit structured geometry is already exposed as part of the generative condition. We therefore propose DRAGOMETRY, a point-based editing framework that performs dragging directly in the geometry condition space rather than through learned feature correspondence. We instantiate the framework on MMDM with FLAME for facial editing. User specified 2D handles are associated with persistent 3D surface points, allowing drag constraints to be resolved through different geometric variables. For local deformation, we optimize FLAME expression and jaw parameters and introduce Jacobian-based parameter weighting to favor parameters relevant to the requested motion while suppressing unwanted deformation elsewhere. For viewpoint edits, we instead optimize camera parameters while preserving the underlying facial geometry. We further introduce DragFace, a benchmark containing both facial deformation and rotation edits, together with Geometry Mean Distance, which evaluates drag accuracy using explicit geometric correspondence. Experiments show that our method achieves more accurate geometric point control, more effective facial deformation, and substantially larger coherent viewpoint changes than existing diffusion-based drag editing methods.