If by "exactly recreate an image" you mean extract a binary-identical reconstruction of the original image from the model, then no. The size of the training data is many, many times larger than the model so if this were possible you would have devised the most amazing lossless compression algorithm known to humanity. So, signs point to no, although perhaps there are some contrived edge cases where it might be possible, such as a large model overfit to a small number of images. I'm not an ML researcher so maybe you should ignore this post but this is really more of an information theory question isn't it?