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Accurate computational up-sampling of CT images grants the benefits of high resolution imaging without the drawbacks of increased scan time and radiation. Among deep learning approaches to medical image super-resolution, CNNs and GANs dominate, but suffer from drawbacks such as texture smoothing and mode collapse. We explore an alternative class of model, a denoising diffusion probabilistic model (DDPM), and demonstrate its ability to recover fine detail in cortical and trabecular bone architecture from computationally undersampled images of ex-vivo bone (upscale factor of 3). By increasing image quality and decreasing scan time and radiation dose, these methods show great potential for clinical use across a variety of imaging modalities.