If you want to avoid Diabolo fee, you can take a train to/from Zaventem. Between Zaventem station and the airport, it's a 30 minuten walk.
To the airport, pass the main roundabout to a second roundabout. Cross the street and follow the cycle path to the Terminal.
From the airport, leave the Terminal building on floor 0 towards the bus station. Cross the bus station. Follow the red painted floor to the first roundabout. Turn left, pass along the main roundabout to the station.
Google Maps