The construct of laissez-faire does away with the protection of collective freedom. Hence, freedom becomes oligarchically and narrowly controlled — quite the opposite of freedom, thus restricting inflation.
Get ready for the straight talk: the supposition of your question is rooted in an economic religion of false truisms.
A free-market cannot remotely be free without paradoxical rules to protect collective freedom from individual freedom. Since the construct of laissez-faire does away with the protection of collective freedom, real freedom cannot exist in a laissez-faire environment (the U.S. is a clear testament to that).
Therefore, any suggested (inverse) correlation between “free-markets” and inflation is void of causation.