You have several options. By default you can save it wherever you think is convenient, it can be a cloud or an image server you trust.

Secondarily #Nostr has some protocols such as the NIP-94 which allows you to save the images or videos as a #Nostr event on a server of your trust or the NIP-95 which allows you to save the images or videos in relays. I think this is the ultimate element of trust, since you can use a public or pay relay, or even create your own relay for your files.