This study aims to improve photon counting CT (PCCT) image resolution using denoising diffusion probabilistic models (DDPM). Although DDPMs have shown superior performance when applied to various computer vision tasks, their effectiveness has yet to be translated to high dimensional CT super-resolution. To train DDPMs in a conditional sampling manner, we first leverage CatSim to simulate realistic lower resolution PCCT images from high-resolution CT scans. Since maximizing DDPM performance is time-consuming for both inference and training, especially on high-dimensional PCCT data, we explore both 2D and 3D networks for conditional DDPM and apply methods to accelerate training. In particular, we decompose the 3D task into efficient 2D DDPMs and design a joint 2D inference in the reverse diffusion process that synergizes 2D results of all three dimensions to make the final 3D prediction. Experimental results show that our DDPM achieves improved results versus baseline reference models in recovering high-frequency structures, suggesting that a framework based on realistic simulation and DDPM shows promise for improving PCCT resolution.