To introduce a model that describes the effects of rigid translation due to respiratory motion in displacement encoding with stimulated echoes (DENSE) and to use the model to develop a deep convolutional neural network to aid in first-order respiratory motion compensation for self-navigated free-breathing cine DENSE of the heart. The motion model includes conventional position shifts of magnetization and further describes the phase shift of the stimulated echo due to breathing. These image-domain effects correspond to linear and constant phase errors, respectively, in k-space. The model was validated using phantom experiments and Bloch-equation simulations and was used along with the simulation of respiratory motion to generate synthetic images with phase-shift artifacts to train a U-Net, DENSE-RESP-NET, to perform motion correction. DENSE-RESP-NET-corrected self-navigated free-breathing DENSE was evaluated in human subjects through comparisons with signal averaging, uncorrected self-navigated free-breathing DENSE, and breath-hold DENSE. Phantom experiments and Bloch-equation simulations showed that breathing-induced constant phase errors in segmented DENSE leads to signal loss in magnitude images and phase corruption in phase images of the stimulated echo, and that these artifacts can be corrected using the known respiratory motion and the model. For self-navigated free-breathing DENSE where the respiratory motion is not known, DENSE-RESP-NET corrected the signal loss and phase-corruption artifacts and provided reliable strain measurements for systolic and diastolic parameters. DENSE-RESP-NET is an effective method to correct for breathing-associated constant phase errors. DENSE-RESP-NET used in concert with self-navigation methods provides reliable free-breathing DENSE myocardial strain measurement.