# Flow-of-Thought

The work introduces Flow-of-Thought (FoT), a framework that trains coordinate-, time-, and action-conditioned spatial U-Nets with flow matching on rotation orbits and cumulative shortest-path prefixes, then freezes the learned dynamics; at inference, the source and its horizontal reflection serve as competing hypotheses selected by foreground-weighted reconstruction energy. On locked tests FoT reaches 100.0% on Tetris and 99.0% on colored shapes, with maze endpoint IoU 97.5% and 100% goal reach; under frozen transfer to 133 BLINK Multi-view public validation pairs, the orbit-trained flow reaches 72.2% versus 63.9% for its endpoint-only control.

The work introduces Flow-of-Thought (FoT), a framework that trains coordinate-, time-, and action-conditioned spatial U-Nets with flow matching on rotation orbits and cumulative shortest-path prefixes, then freezes the learned dynamics; at inference, the source and its horizontal reflection serve as competing hypotheses selected by foreground-weighted reconstruction energy. On locked tests FoT reaches 100.0% on Tetris and 99.0% on colored shapes, with maze endpoint IoU 97.5% and 100% goal reach; under frozen transfer to 133 BLINK Multi-view public validation pairs, the orbit-trained flow reaches 72.2% versus 63.9% for its endpoint-only control.