OsteoFlow: Lyapunov-Guided Flow Distillation for Predicting Bone Remodeling after Mandibular Reconstruction

Predicting long-term bone remodeling after mandibular reconstruction would be of great clinical benefit, yet standard generative models struggle to maintain trajectory-level consistency and anatomical fidelity over long horizons, particularly in low-data regimes. We introduce OsteoFlow, a flow-based framework predicting Year-1 post-operative CT scans from Day-5 scans. Our core contribution is Lyapunov-guided trajectory distillation: Unlike one-step distillation, our method distills a continuous trajectory over transport time from a registration-derived stationary velocity field teacher. Combined with a resection-aware image loss, this enforces geometric correspondence without sacrificing generative capacity. Evaluated on 344 paired regions of interest, OsteoFlow significantly outperforms state-of-the-art baselines, reducing mean absolute error in the surgical resection zone by ~20%. This highlights the promise of trajectory distillation for long-term prediction in low-data clinical settings. Code is available on GitHub: https://github.com/hamidreza-aftabi/OsteoFlow.