Triangular Consistency as a Universal Constraint for Learning Optical Flow

We propose triangular consistency as a first-principled con-straint for optical flow, which is agnostic to network architecture, super-vision type, and dataset, and applies to both image-pair and multi-framesettings. This simple but powerful constraint is to compose two flows toinduce a third flow and enforce consistency among the three. The com-posed flows may arise from (i) image pairs, yielding cycle consistency; (ii)multiple video frames, producing longer-range motion through temporalchaining; or (iii) image pairs combined with controlled synthetic transfor-mations, which becomes data augmentation. This triangular consistencyintroduces negligible computational overhead and requires no additionalannotations. Since it is derived directly from the geometry of opticalflow, it does not rely on model-specific assumptions and serves as a “uni-versal” plug-and-play component for optical flow training. Experimentsshow consistent improvement across supervised, unsupervised, and trans-fer learning settings. Code: https://github.com/lsuvision/tri-flow.