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

arXiv: https://arxiv.org/abs/2603.22421 · HTML: https://mlsanity.com/paper/2603.22421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [ResUNet++: An Advanced Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1911.07067/) (2019)
- [MAISI: Medical AI for Synthetic Imaging](https://mlsanity.com/paper/2409.11169/) (2024)
- [Anatomically-Controllable Medical Image Generation with Segmentation-Guided Diffusion Models](https://mlsanity.com/paper/2402.05210/) (2024)
- [Adaptive Latent Diffusion Model for 3D Medical Image to Image Translation: Multi-modal Magnetic Resonance Imaging Study](https://mlsanity.com/paper/2311.00265/) (2023)
- [Cross-conditioned Diffusion Model for Medical Image to Image Translation](https://mlsanity.com/paper/2409.08500/) (2024)
- [MedVAE: Efficient Automated Interpretation of Medical Images with Large-Scale Generalizable Autoencoders](https://mlsanity.com/paper/2502.14753/) (2025)
- [DIFR3CT: Latent Diffusion for Probabilistic 3D CT Reconstruction from Few Planar X-Rays](https://mlsanity.com/paper/2408.15118/) (2024)
- [CIResDiff: A Clinically-Informed Residual Diffusion Model for Predicting Idiopathic Pulmonary Fibrosis Progression](https://mlsanity.com/paper/2408.00938/) (2024)
- [ClinicalFMamba: Advancing Clinical Assessment using Mamba-based Multimodal Neuroimaging Fusion](https://mlsanity.com/paper/2508.03008/) (2025)

## Abstract (arXiv)

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.