In /etc/pam.d/gdm add the following line, right above the line @include common-auth
auth sufficient pam_listfile.so sense=allow file=/etc/passwordless item=user
Create a file /etc/passwordless with one line for the username, which is allowed to login without password, e.g.:
media
In Gnome, select Desktop -> Administration -> Login Window:
Select a theme with a face browser, e.g. "Happy GNOME with Browser"