You'll be pleased to know that Adobe does allow the user to download their generated images! At the moment you can only download them with the Firefly watermark included in the bottom left corner, and the images cannot be used for commercial use. But you can still download your images.
To do this, first you need to generate your images. When the images are finished generating, hover your cursor over whichever image you want to download. This will bring up a few options for the image. The download button is the 2nd one in on the top right hand side, next to the favourites option.
Hope this helps! If you're still having problems let me know and I'll see if I can help.