Local differential privacy algorithms combined with deep generative models can enhance secure medical image sharing among researchers in the public domain without central administrators, but those were limited to the generation of low-resolution images, which are very insufficient for diagnosis by medical doctors. To enhance the performance of deep generative models so that they can generate high-resolution medical images, we propose a large-scale diffusion model that can, for the first time, unconditionally generate high-resolution ($256\times 256 \times 256$) volumetric medical images. We specifically adopted head magnetic resonance images, but we trained the model without knowledge intrinsic for medical images; hence, we can apply the models to natural images. This diffusion model has 19 billion parameters, but to make it easy to train it, we temporally divided the model into 200 submodels, each of which has 95 million parameters. Moreover, on the basis of this new diffusion model, we propose another formulation of image anonymization with which the processed images can satisfy provable Gaussian local differential privacy and with which we can generate images semantically different from the original image but belonging to the same class. We believe that the formulation of this new diffusion model and the implementation of local differential privacy algorithms combined with the diffusion models can contribute to the secure sharing of practical images upstream of data processing.