\vspace{-3mm}
\section{Conclusion}
The proposed \model~framework serves as a plug-and-play solution, enhancing existing registration networks for improved anatomical accuracy and interpretability across synthetic and medical imaging datasets. It provides a compact statistical representation of deformation fields, aiding downstream tasks like morphological analysis and population studies. Future work could focus on incorporating diagnostic and clinical covariates to enhance the diffeomorphic analysis framework.~\model's inherent computational efficiency makes it a promising candidate for extension to 3D registration tasks.


\midlacknowledgments{
This work was supported by the National Institutes of Health under grant numbers NIH-R01CA259686 (Sarang Joshi) and NIH-R01DE032366 (Shireen Elhabian).}