Would one say that indifference curves decrease since consumers prefer diversity?

When you say that indifference curves “decrease,” I assume that you are referring to the fact that they have negative slopes.  In other words, they slope downward from left to right.  I would not say that they slope downward because people prefer diversity. Instead, I would say that they slope downward because an indifference curve assumes a constant level of utility and people get more utility from consuming more of a given good.

An indifference curve shows us the various levels of two goods that a consumer could consume without changing his or her level of utility. When we make such a curve, we assume that the consumer actually wants both goods.  In other words, consuming more of a good would increase his or her utility. However, this causes a problem. We are saying that a consumer gains utility from consuming more of a good, but we have to keep that consumer’s utility unchanged.  In order to do this, we have to make our indifference curve slope downward. 

Let us imagine an indifference curve with apples and oranges as the two products the consumer can consume.  The consumer likes both apples and oranges so her utility would increase if she consumed more oranges. However, the definition of an indifference curve tells us that her utility has to stay the same. Therefore, as she consumes more oranges (thus increasing her utility) she has to consume fewer apples at the same time (dropping her utility and thus keeping it constant even as she eats more oranges).  This (and not a preference for diversity) is the real reason why the indifference curve has to slope downward.  It has to keep utility constant even as a person consumes more of one good.