In respiratory disorders such as thoracic insufficiency syndrome (TIS), the quantitative study of the regional motion of the left hemi-diaphragm (LHD) and right hemi-diaphragm (RHD) can give detailed insights into the distribution and severity of the abnormalities in individual patients. Dynamic magnetic resonance imaging (dMRI) is a preferred imaging modality for capturing dynamic images of respiration since dMRI does not involve ionizing radiation and can be obtained under free-breathing conditions. Using 4D images constructed from dMRI of sagittal locations, diaphragm segmentation is an evident step for the said quantitative analysis of LHD and RHD in these 4D images. In this paper, we segment the LHD and RHD in three steps: recognition of diaphragm, delineation of diaphragm, and separation of diaphragm along the mid-sagittal plane into LHD and RHD. The challenges involved in dMRI images are low resolution, motion blur, suboptimal contrast resolution, inconsistent meaning of gray-level intensities for the same object across multiple scans, and low signal-to-noise ratio. We have utilized deep learning (DL) concepts such as Path Aggregation Network and Dual Attention Network for the recognition step, Dense-Net and Residual-Net in an enhanced encoder-decoder architecture for the delineation step, and a combination of GoogleNet and Recurrent Neural Network for the identification of the mid-sagittal plane in the separation step. Due to the challenging images of TIS patients attributed to their highly distorted and variable anatomy of the thorax, in such images we localize the diaphragm using the auto-segmentations of the lungs and the thoraco-abdominal skin. We achieved an average±SD mean-Hausdorff distance of ∼3±3 mm for the delineation step and a positional error of ∼3±3 mm in recognizing the mid-sagittal plane in 100 3D test images of TIS patients with a different set of ∼430 3D images of TIS patients utilized for building the models for delineation, and separation. We showed that auto-segmentations of the diaphragm are indistinguishable from segmentations by experts, in images of near-normal subjects. In addition, the algorithmic identification of the mid-sagittal plane is indistinguishable from its identification by experts in images of near-normal subjects. Motivated by applications in surgical planning for disorders such as TIS, we have shown an auto-segmentation set-up for the diaphragm in dMRI images of TIS pediatric subjects. The results are promising, showing that our system can handle the aforesaid challenges. We intend to use the auto-segmentations of the diaphragm to create the initial ground truth (GT) for newly acquired data and then refining them, to expedite the process of creating GT for diaphragm motion analysis, and to test the efficacy of our proposed method to optimize pre-treatment planning and post-operative assessment of patients with TIS and other disorders.