Oh really? Just because the lack of a central administration makes it impossible to intentionally induce inflation doesn't mean that it can't happen. If inflation was impossible, that means that I wouldn't be able to adjust the price in bitcoins of my product based on demand, which is obviously not true. Hence, it is possible that the average price in bitcoins of everything which can be purchased by bitcoins rises, which means inflation.
Inflation is possible, but inflation would be the direct result of the transaction system, which creates the bitcoins, hence a fully closed fiat system. No one can influence it, everything happens because of itself. Even the scale of production of bitcoins is fundamentally opposed to inflation (however, may cause deflation)
Also, you are confusing inflation of currency with inflation of an individual price. An inflation of currency will cause an inflation of all prices, but an inflation of price will not cause an inflation of currency (unless for all products on the market). Inflation of currency is something like what happened to the German Mark after WWI, inflation of prices is what happens because of supply and demand, but only effects a small section of the market. This kind of inflation generally will not spiral out of control, because as demand for one thing goes up, due to a short-term fixed income of consumers, demand for another thing must go down, making the market basket maintain the same price.
A rise in all prices can only happen when there is a devaluing of a currency, which stalls transactions, which reduces bitcoin production, which causes the bitcoin to gain value (unless it is in a downward spiral, in which case the system would kill itself).