According to the AS/AD Model and the wealth effect, as the price level falls, ceteris paribus, people will in effect be richer and will

I believe that the answer that you are looking for is that people will spend more money by buying more goods and services.  This will cause aggregate demand to increase.

The reason for this is that people will feel richer.  They will feel as if they can afford to buy more things.  Since consumer spending is a huge part of aggregate demand, an increase in consumer spending will lead to a great deal more aggregate demand.

Consumer confidence, which is affected to a large degree by such things as the wealth effect, is a major influence on the level of aggregate demand.  So a decline in the CPI, which will increase consumer confidence, will lead to more spending as well.