Nice goalpost shift. From "inflation didn't exist at all" to "trend inflation didn't exist".
Anyway, blaming "fiat" is an absolutely retarded take and you would be better served in a 2012 /pol/ Ron Paul thread than here. All money (in sufficiently developed economies) is created by fiat, because money is created through debt and loans. The more banks decide to lend, the more money gets created. Even in the days of gold-tied currencies, most money was NOT backed by actual hard specie — which resulted in repeated financial crises in countries without a central financial coordinator, e.g. USA.
The "introduction" of "fiat currency" wasn't a transformative change, but simply the state acknowledging and formalizing what already happens in practice.
The real reason that "trend inflation" started after the Great Depression is Keynesianism. Mid-century capitalism had two overarching tendencies that impacted pricing:
1. Full employment and a strong labor movement created wage-driven inflation, i.e. porkies would keep raising prices to maintain profit margins in the face of rising worker compensation.
2. Stimulus. Instead of leaving money-creation to the bankers, state capitalist governments begun directly engaging in permanent mass borrowing and spending, which tended to push effective demand faster than actual economical value was being created (as was its purpose).
Note that neither of these are dependent on "fiat currency". Indeed, the Bretton Woods system still had the USD tied to gold and world currencies pegged against the it right up to the 1970's. Both money creation and price raising (two somewhat correlative
but not causative
phenomena, I'd like to emphasize) were unhindered by this. In fact, the reason Nixon took the dollar officially off the gold standard was because there was fear that if people actually tried to redeem their gold, it would instigate a massive financial crisis and a political fiasco. As I said above, it was an acknowledgement of reality rather than a proactive move.
Speaking of the 1970's, it was a decade when wage-driven inflation in particular blew up. and it wasn't until neoliberalism came into being and crushed workers that it subsided. The nature of stimulus also changed — governments still maintain permanent deficits, but they also increasingly rely on CBs manipulating interest rates to keep porkies' monetary profits ever-so-slightly above the actual surplus value they are capable of extracting.
This is reflected in the fact that after the 1980's, official inflation rates tend to be low and stable compared to the postwar state capitalist "golden age".