Navigating in human-filled public spaces is a critical challenge for deploying autonomous robots in real-world environments. This paper introduces NaviDIFF, a novel Hamiltonian-constrained socially-aware navigation framework designed to address the complexities of human-robot interaction and socially-aware path planning. NaviDIFF integrates a port-Hamiltonian framework to model dynamic physical interactions and a diffusion model to manage uncertainty in human-robot cooperation. The framework leverages a spatial-temporal transformer to capture social and temporal dependencies, enabling more accurate spatial-temporal environmental dynamics understanding and port-Hamiltonian physical interactive process construction. Additionally, reinforcement learning from human feedback is employed to fine-tune robot policies, ensuring adaptation to human preferences and social norms. Extensive experiments demonstrate that NaviDIFF outperforms state-of-the-art methods in social navigation tasks, offering improved stability, efficiency, and adaptability11The experimental videos and additional information about this work can be found at: https://sites.google.com/view/NaviDIFF.