Yes any essential oils including regular essential oils can easily be used in a diffuser.
You don't need to put any special essential oils or diffuser oils into your diffuser as plain old essential oils that you use for other things can be placed in the diffuser to be dispersed into the air.
For a good nights sleep I diffuse Lavender Essential oil in my diffuser at night and then diffuse lemon and other essential oils during the day depending on what essential oils I choose to use that day.
So if you have a diffuser and want to put any of your essential oils in it to diffuse you certainly can.