In the app’s Terms of Service, they note that FaceApp users own their own content. This is based on this particular section which reads, “Except for the license you grant below, you retain all rights in and to your User Content, as between you and FaceApp. Further, FaceApp does not claim ownership of any User Content that you post on or through the Services.”
However, upon further inspection of the license that you’ll be granting the app, it seems that you actually won’t own the rights to your photos. “You grant FaceApp a perpetual, irrevocable, nonexclusive, royalty-free, worldwide, fully-paid, transferable sub-licensable license to use, reproduce, modify, adapt, publish, translate, create derivative works from, distribute, publicly perform and display your User Content and any name, username or likeness provided in connection with your User Content in all media formats and channels now known or later developed, without compensation to you.”
This means that in theory, FaceApp could use the photos that you have uploaded to its servers for processing. They could use it for advertisements and not have to pay you a single cent. The app has come under fire over alleged privacy concerns, and these terms of services certainly do not help its cause, so it’s something to think about if you plan on using it.