We propose an OCT super-resolution framework based on a plug-and-play diffusion model (PnP-DM) to reconstruct high-quality images from sparse measurements (OCT B-mode corneal images). Our method formulates reconstruction as an inverse problem, combining a diffusion prior with Markov chain Monte Carlo sampling for efficient posterior inference. We collect high-speed under-sampled B-mode corneal images and apply a deep learning-based up-sampling pipeline to build realistic training pairs. Evaluations on in vivo and ex vivo fish-eye corneal models show that PnP-DM outperforms conventional 2D-UNet baselines, producing sharper structures and better noise suppression. This approach advances high-fidelity OCT imaging in high-speed acquisition for clinical applications.