Currently he falls asleep in my arms and then I put him down.
Your first step wants to be lie down with him in your arms on the bed and go to sleep there. Stay until asleep.
Next step is just have arms over him going to sleep (still lying next time him cuddled up), but not arms all the way around him. Stay until asleep.
Next work on just lying next to him, face to face and close, but just your hand on his chest/shoulder as he goes to sleep. Stay until asleep.
Next stay physically close and put hand on chest/shoulder to settle but remove hand when settled. But stay close and facing him - the idea is to reduce physical contact as he falls asleep. Stay until asleep.
Next step is take your phone or a book with you. Settle him with your hand, then remove hand and make sure he's settled, then turn onto your back or front so your not facing him. Do something else so he knows you're close, but leaving him to it to go to sleep on his own. If he fussed, roll back over and resettle with hand. But retreat back once settled. Stay until asleep.
Next step - roll away and face away from him but still on bed while he goes to sleep. Phone or book so he gets that you are physically there, but he's going to sleep without you. Roll back if unsettled, retreat when settled. Stay until asleep.
Next step - sit up in bed once he's settled. Stay until asleep.
Next - stand next to bed. Return to lying if unsettled but retreat once settled. Stay until asleep.
Next - wait in doorway until he's asleep
Next - have "jobs" to do upstairs so you keep popping away from door for a minutes or do. But always go back. Gradually extend the time and frequency these jobs take - but conmitt to saying upstairs until he's asleep. If he needs you, so straight back in and resettle on bed. But always retreat back once he's settled.
He has to trust that you'll always/stay until he is asleep and will be there the moment he needs you. So always stick around until he's asleep. In time he'll need you less and you can start going downstairs after settling him.