Accurately reconstructing the sound field inside of a room purely from real-world data is extremely time-consuming, requiring large measurement campaigns. In the past decade, several signal-processing-based techniques have been proposed to predict the sound field within a region from limited measurements. More recently, data-driven methods have also been proven to be powerful tools for this task. In this work, SFR3 (Sound Field Reconstruction via Repeated Refinement) is proposed, based on an existing diffusion image super-resolution model, which reconstructs the sound field from a grid of uniformly spaced microphones, in contrast to the randomized distribution assumed by several state-of-the-art techniques. The model's performance is compared to a naive baseline consisting of a bicubic interpolation, a kernel-based method commonly used for this task, and a data-driven approach using a complex-valued U-Net, showing that the proposed method outperforms, in terms of normalized mean squared error, the aforementioned techniques, especially at lower frequencies.