Refractive index gradients in materials or at material interfaces lead to x-ray diffraction. Interference of this radiation with adjacent x-ray waves causes phase contrast that can be used for imaging purposes if an x-ray source with sufficient spatial coherence is used. The imaging modality presented here uses hard x radiation diffracted at interfaces, but requires only little spatial coherence. We report experiments showing, first, that image contrast is not diminished by motional blurring, and second, that contrast can be increased by orders of magnitude relative to in-line x-ray phase-contrast imaging. These properties substantially broaden the applicability of phase-sensitive imaging to moving samples and very weak density gradients.