Cardiovascular magnetic resonance imaging is a powerful diagnostic tool for assessing cardiac structure and function. Traditional breath-held imaging protocols, however, pose challenges for patients with arrhythmias or limited breath-holding capacity. We introduce Motion-Guided Deep Image prior (M-DIP), a novel unsupervised reconstruction framework for accelerated real-time cardiac MRI. M-DIP employs a spatial dictionary to synthesize a time-dependent template image, which is further refined using time-dependent deformation fields that model cardiac and respiratory motion. Unlike prior DIP-based methods, M-DIP simultaneously captures physiological motion and frame-to-frame content variations, making it applicable to a wide range of dynamic applications. We validate M-DIP using simulated MRXCAT cine phantom data as well as free-breathing real-time cine and single-shot late gadolinium enhancement data from clinical patients. Comparative analyses against state-of-the-art supervised and unsupervised approaches demonstrate M-DIP's performance and versatility. M-DIP achieved better image quality metrics on phantom data, as well as higher reader scores for in-vivo patient data.