Diffraction-enhanced imaging (DEI) is an emerging x-ray imaging method that simultaneously yields x-ray attenuation and refraction images and holds great promise for soft-tissue imaging. The DEI has been mainly studied using synchrotron sources, but efforts have been made to transition the technology to more practical implementations using conventional x-ray sources. The main technical challenge of this transition lies in the relatively lower x-ray flux obtained from conventional sources, leading to photon-limited data contaminated by Poisson noise. Several issues that must be understood in order to design and optimize DEI imaging systems with respect to noise performance are addressed. Specifically, we: (a) develop equations describing the noise properties of DEI images, (b) derive the conditions under which the DEI algorithm is statistically optimal, (c) characterize the imaging performance that can be obtained as measured by task-based metrics, and (d) consider image-processing steps that may be employed to mitigate noise effects.