Cardiac DTI provides invaluable information about the state of myocardial microstructure. Motion and systematic signal variations of the imaging process influence the tensor inference. Image registration prior to tensor fitting with an LSQ estimator is the common data processing approach. The feasibility of training a neural network with simulated data modelling tensors and slice misalignment due to free breathing for inference of diffusion tensors from free-breathing in vivo data is investigated. Evaluation on simulated test data demonstrates feasibility of the training process. Application to in vivo data shows promising results of the CNN especially at myocardial borders.