Vectile: Learning Reusable Transport References for Counterfactual Generation

A visual reference shows a response under particular conditions; editing often requires that response under another stimulus, installation, or arrangement of interacting objects. We introduce transport references: reusable local responses rather than the trajectories or illumination patterns observed in a reference. VECTILE extracts a response tile, installs it at a target site, and rolls out the installed tiles through TILEFLOW, where the target repeatedly supplies their current inputs and states. Visual synthesis then expresses the resulting consequence in images or videos. We show that this separation supports both optical interactions, where outgoing influence changes what other sites receive, and active-material deformation, where changing shape alters subsequent exposure. Our optical implementation couples local response and typed transport to spatial-goal-guided diffusion; the material implementation supplies camera-specific controls from one shared predicted world trajectory. Across 68 configurations of a held-out active-material world, VECTILE produces 52 correct edits versus 6 for our VIPER-style/Wan implementation, with 16 low-visibility configurations. On a relighting benchmark, VECTILE recovers seven edits missed by our natively adopted LightMover-style/Wan baseline.