Image synthesis in magnetic resonance (MR) imaging has been an active area of research for more than ten years. MR image synthesis can be used to create images that were not acquired or replace images that are corrupted by artifacts, which can be of great benefit in automatic image analysis. Although synthetic images have been used with success in many applications, it is quite often true that they do not look like real images. In practice, an expert can usually distinguish synthetic images from real ones. Generative adversarial networks (GANs) have significantly improved the realism of synthetic images. However, we argue that further improvements can be made through the introduction of noise in the synthesis process, which better models the actual imaging process. Accordingly, we propose a novel approach that incorporates randomness into the model in order to better approximate the distribution of real MR images. Results show that the proposed method has comparable accuracy with the state-of-the-art approaches as measured by multiple similarity measurements while also being able to control the noise level in synthetic images. To further demonstrate the superiority of this model, we present results from a human observer study on synthetic images, which shows that our results capture the essential features of real MR images.