We present a method for diffusion tensor MRI in the beating heart that is insensitive to cardiac motion and strain. Using a stimulated echo pulse sequence with two electrocardiogram (ECG) triggers, diffusion-encoding bipolar gradient pulses are applied at identical phases in consecutive cardiac cycles. In this experiment, diffusion is encoded at a single phase in the cardiac cycle of less than 30 ms in duration. This encoding produces no phase shifts for periodic motion and is independent of intervening strains. Studies in a gel phantom with cyclic deformation confirm that by using this sequence we can map the diffusion tensor free of effects of cyclic motion. In normal human subjects, myocardial diffusion eigenvalues measured with the present method showed no significant change between acquisitions encoded at maximum contractile velocity (peak) vs. at myocardial standstill (end-systole), demonstrating motion independence of in vivo diffusion measurements. Diffusion tensor images acquired with the present method agree with registered data acquired with a previous cardiac diffusion MRI method that was shown to be valid in the normal heart, strongly supporting the validity of MRI diffusion measurement in the beating heart. Myocardial sheet and fiber dynamics measured during systole showed that normal human myocardial sheet orientations tilt toward the radial during systole, and fiber orientations tilt toward the longitudinal, in qualitative agreement with previous invasive studies in canines. These results demonstrate the technique's ability to measure myocardial diffusion accurately at any point in the cardiac cycle free of measurable motion effect, as if the heart were frozen at the point of acquisition.