Reality is a dance between rigid constraints and deformable structures. For video models, that means generating motion that preserves fidelity as well as structure. Despite progress in diffusion models, producing realistic structure-preserving motion remains challenging, especially for articulated and deformable objects such as humans and animals. Scaling training data alone, so far, has failed to resolve physically implausible transitions. Existing approaches rely on conditioning with noisy motion representations, such as optical flow or skeletons extracted using an external imperfect model. To address these challenges, we introduce an algorithm to distill structure-preserving motion priors from an autoregressive video tracking model (SAM2) into a bidirectional video diffusion model (CogVideoX). With our method, we train SAM2VideoX, which contains two innovations: (1) a bidirectional feature fusion module that extracts global structure-preserving motion priors from a recurrent model like SAM2; (2) a Local Gram Flow loss that aligns how local features move together. Experiments on VBench and in human studies show that SAM2VideoX delivers consistent gains (+2.60% on VBench, 21-22% lower FVD, and 71.4% human preference) over prior baselines. Specifically, on VBench, we achieve 95.51%, surpassing REPA (92.91%) by 2.60%, and reduce FVD to 360.57, a 21.20% and 22.46% improvement over REPA- and LoRA-finetuning, respectively. The project website can be found at https://sam2videox.github.io/ .