Yes, Smart Media Tokens (SMTs) will have inflation.
Here, when we use the term inflation, we are talking about the "printing" of additional tokens after the initial distribution, rather than the everyday definition of inflation as an increase of the prices of goods (which can result from an increase in the supply of money).
Bitcoin is often called a deflationary cryptocurrency since it has a finite supply of 21 million coins. Although it does in fact have a period of inflation with new coins mineable until 2040 prior to becoming deflationary. Steem has inflation at a rate which decreases over time.
For SMTs the inflation rate will be parametrisable with the possibility for the rate to change over time or to be expressed as a percentage of the overall supply.
I think that the inflation parameters will have to be defined in advance. However even if this is the case there is nothing to stop a dApp launching multiple SMTs at later dates. The utility of the token, ie. how it can be used and what rights it reserves, will be just as important as the inflation.
You can read all about SMT inflation on page 29 of the white paper: