Does inflation cause the Aggregate demand curve to shift

hi - just trying to get my head around the causes/effect of inflation vs Aggregate demand. i could be way off in my understanding so please shoot me down if so.

the Aggregate demand curve has Price on the vertical and real GDP on the horizontal, does a price change just cause you to go along the curve? when would a change in inflation / expected inflation cause the aggregate demand curve to shift?

my thinking is that a pure price change doesn’t cause a shift in the curve. a rise in expected inflation would cause real interest rates to drop which would cause companies to invest more, shifting the curve to the right. further, if inflation comes in at an unexpected level, this could have the impact of “fake” demand causing companies to produce more (assuming inflation was greater than expected) shifting the curve to the right in the short term, but as inventories built production would be scaled back causing deflationary pressures.

thanks in advance