Head motion is a major source of image artifacts in head computed tomography (CT), degrading the image quality and impacting diagnosis. Image-domain-based motion correction is practical for routine use since it doesn't rely on hard-to-obtain CT projection data. However, existing convolutional neural network (CNN)-based methods tend to over-smooth images, particularly in cases of moderate to severe 3D motion artifacts. Motivated by the improved image quality and more stable training of diffusion-based generative models, we propose a novel 3D head CT motion correction approach based on conditional diffusion, named HeadMotion-EDM(HM-EDM). This approach has three features. Firstly, we utilize motion-corrupted images as the conditional input. Secondly, we leverage the advanced Elucidated Diffusion Model (EDM) framework, which integrates several pivotal engineering improvements in the diffusion model and significantly expedites the sampling process. Thirdly, we design an efficient 3D-patch-wise training method for 3D CT data. Comparative studies demonstrate that our approach surpasses CNN-based techniques as well as the denoising diffusion probabilistic model (DDPM) in both simulation and phantom studies. Furthermore, radiologists reviewed the results of applying HM-EDM to real-world portable head CT scans, showing its effectiveness in eliminating motion artifacts and improving diagnostic value.