Magnetic resonance (MR) images are often acquired as aniso-tropic volumes in clinical settings. Such volumes have a worse through-plane resolution than in-plane resolution, hampering results in many processing pipelines that expect isotropic resolutions. Super-resolution (SR) is a promising methodology to address this problem, but there is concern whether the estimated high-resolution (HR) image suffers from egregious hallucinations, especially with deep learning methods that produce aesthetically pleasing results. One approach to restrict the impact of hallucinations is to guarantee that the estimated HR image is exactly cycle-consistent with the low-resolution observation. The denoising diffusion null space model (DDNM) achieves this through a range null space decomposition, but the specific design of the forward map is left to the application. In this work, we analyze the forward problem in 2D MR acquisition and construct an appropriate linear map A. We train a denoising diffusion probabilistic model on T \(_1\) -weighted (T \(_1\) -w) head MR images from multiple datasets and implement DDNM using A for the SR task. We show that the approach yields exact cycle-consistent solutions that are also realistic. We evaluated the approach in a wide variety of T \(_1\) -w MR datasets, including withheld subjects from training sites and two sites outside of the training domain. We achieve excellent qualitative and quantitative results according to both distortion and perceptual metrics.