The fact that Stable Diffusion v1.x models memorize images is noted in the various v1.x model cards. For example, the following text is from the Stable Diffusion v1.5 model card:

>No additional measures were used to deduplicate the dataset. As a result, we observe some degree of memorization for images that are duplicated in the training data. The training data can be searched at https://rom1504.github.io/clip-retrieval/ to possibly assist in the detection of memorized images.