In a magnetic resonance apparatus and a method and controller for operating such an apparatus, first and second diffusion-weighted image data are reconstructed from first and second diffusion-encoded raw data that were respectively acquired using different diffusion-encoding gradient pulse sub-sequences. The different sub-sequences differ by respectively having a different parameter that characterizes the respective sub-sequence as a function of time. The first and second reconstructed image data are compared and a deviation of the image data from normal Gaussian diffusion behavior is determined model-free on the basis of the comparison result.