Yes, there will be some noise associated with riding your bike indoors on a cycling trainer! Sound acts differently off walls/ceilings than it does on the road in an open environment. Of course, there are a couple of solutions that folks have found helpful;

One idea is to pick up an exercise/trainer mat and place it under the trainer while it is in use. These mats are designed specifically to dampen the vibration and lessen noise caused by cycling trainers. They also have the added benefit of sparing your floor from scratches or flying sweat! 

Another idea is to replace the rear tire of your bike with a slick, or racing tire. The lack of tread on these tires reduces noise as well.