Cellulose

No insulation "attracts" moisture, but various materials exhibit different moisture handling characteristics. Cellulose insulation is a "storage layer" in an assembly. This means it can safely hold moisture that might otherwise move into more vulnerable parts of the assembly and still maintain its thermal resistance. Exfiltration of  moisture-laden air into walls and ceilings is the major moisture transfer mechanism. The low air permeability of cellulose all but eliminates this means of moisture  movement. In a paper presented at a 1999 conference two of the world's leading moisture experts reported data based on computer modeling that showed cellulose insulation in a wall resulted in lower moisture levels in other wall components than in an uninsulated wall.