Set - value bet or check behind against 4 opponents and drawy board

[obi_wang]

Preflop: Hero is Button with 10 [img]/images/graemlins/spade.gif[/img], 10 [img]/images/graemlins/heart.gif[/img].
Hero raises pre-flop, with 5-6 callers.

Flop: 10 [img]/images/graemlins/diamond.gif[/img], 7 [img]/images/graemlins/diamond.gif[/img], 3 [img]/images/graemlins/spade.gif[/img]
MP bets, 3 callers, Hero raises, all 4 players call.

Turn: 4 [img]/images/graemlins/diamond.gif[/img]
Line Check. I decide to check behind on button fearing a check-raise, since one of my 4 opponents HAS to have 2 diamonds, right? Hoping to fill up on river cheaply.


River: J [img]/images/graemlins/heart.gif[/img]
Check, check, check, check. Value bet or check behind?

Comments on turn and river appreciated.