Better than JPEG? Researcher discovers that Stable Diffusion can compress images

It's certainly possible to train an autoencoder with enough data to make it a reliable compression engine, provided you have a way to deal with all resolutions. Once the training and validation were done, I expect you'd get somewhat better than JPEG compression at some cost in compute more than JPEG. A standard implementation and weights would be all that were required to be agreed on at that point.

I wouldn't use stable diffusion for that task.

I wouldn't really call that compression any more than a bad witness recounting of an event. Reminds me of that photocopier with that could scan more into memory but had a habit of flipping digits in the output copies with strokes that clearly were not present on the input.