Every picture you take with Instagram is saved on the phone. Take a picture, optionally apply a filter, hit next, but don't hit Upload. Go to the Gallery app and you'll see an Instagram folder with your filtered photo, and a copy of the original photo in the Camera folder.

You are right, I was wrong: didn't see this folder.

This definitely isn't the case on iOS. I use instagram all the time, but only for the filters. Pictures I take with it get put on dropbox.

you can save. at least on iOS, tou can.