I don't think that dividends are typically coupled to inflation. The return on an investment (at least via stock ownership) includes dividends + asset appreciation, right? I would expect the combination to be related to inflation but not necessarily dividends alone. Is that the right way to think about it? I'm not a finance guy.
An idealized company in a static market that has been making the same real (i.e. inflation adjusted) profits for a while and is expected to for quite some time will have its price track inflation, so any dividends paid out will be on top of inflation.
Real life is much messier than the above, due to things like speculation (how much some people think other people will think the company will be worth in a year), changes in the broader market (if the "zero risk" rate of returns goes up or down, then equities, which have higher risk will tend to move in the opposite direction), and such can have drastic effects on a company's market value.
