Diffusion models were initially developed for text-to-image generation and are now being utilized to generate high quality synthetic images. Preceded by GANs, diffusion models have shown impressive results using various evaluation metrics. However, commonly used metrics such as FID and IS are not suitable for determining whether diffusion models are simply reproducing the training images. Here we train StyleGAN and a diffusion model, using  BRATS20, BRATS21 and a chest x-ray pneumonia dataset, to synthesize brain MRI and chest x-ray images, and measure the correlation between the synthetic images and all training images. Our results show that diffusion models are more likely to memorize the training images, compared to StyleGAN, especially for small datasets and when using 2D slices from 3D volumes. Researchers should be careful when using diffusion models (and to some extent GANs) for medical imaging, if the final goal is to share the synthetic images.