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Objective. We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary magnetic resonance imaging. Approach. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Main results. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans. Significance. The proposed unsupervised motion-compensated scheme jointly estimates the latent vectors that capture the motion dynamics, the corresponding deformation maps, and the reconstructed motion-compensated images from the raw k-t space data of each subject. Unlike current motion-resolved strategies, the proposed scheme is more robust to bulk motion events during the scan. [ABSTRACT FROM AUTHOR]