Where are my recorded Diorama videos saved?

After you press Record Video on the top right of the window to create a quilt recording of your scene. You'll be saving out a nice 10-second loop of your scene in Diorama. The folder in which it saves Documents\Diorama\VideoRecordings will automatically open up once the process is completed.

Here is the full tutorial that walks you through the entire process from start to finish.