Abstract: Simulation-to-real transfer remains a central challenge in robotics, as mismatches between simulated and real-world dynamics often lead to failures. While reinforcement learning offers a principled mechanism for adaptation, existing sim-to-real finetuning methods struggle with exploration and long-horizon credit assignment in the low-data regimes typical of real-world robotics. We introduce \texttt{Simulation Distillation} (\texttt{SimDist}), a sim-to-real framework that distills structural priors from a simulator into a latent world model and enables rapid real-world adaptation via online planning and supervised dynamics finetuning. By transferring reward and value models directly from simulation, \texttt{SimDist} provides dense planning signals from raw perception without requiring value learning during deployment. As a result, real-world adaptation reduces to short-horizon system identification, avoiding long-horizon credit assignment and enabling fast, stable improvement. Across precise manipulation and quadruped locomotion tasks, \texttt{SimDist} substantially outperforms prior methods in data efficiency, stability, and final performance.