Remember that the Fed doesn't really create all money - it creates monetary base, and then bank lending creates the vast amount of "money" that is "in circulation." In a typical situation, if the Fed doubles the monetary base, M1 increases by 2 or 2.5 times, depending on the multiplier (which refers to how many times $1 is lent by a bank, re-lent by another, etc etc). In a deflationary environment, the multiplier can be low, so that doubling the monetary base may only increase M1 by 10% or 50%. That's why deflation is so hard to control or stop - it's not the Fed doing it, it's the Fed losing control of its usual mechanism - as predictable in a fiat, credit-based monetary system as inflation, but not as infrequent.
And then there's today...
Last year, the Fed **more than** doubled the base, and money supply barely budged - every measure including M1, M2 and MZM turned slighty up and then shrugged it off. As a matter of fact, the numbers claim that monetary base EXCEEDED M1 for a period of time, and that today monetary base and M1 are about equal. That's unheard of, and I don't understand how it's even definitionally possible.
But here it is in its absurd and freightening glory:
(Note that in order to better visualize the ratios, Base & M1 are on the left axis, M2 & MZM on the right)
Will all that base money come flying back at us as inflation eventually? If our formal banking system and "shadow banking" system return to anything near their previous selves, yes. I'm not holding out much hope of that for a few years, but it pays to be prepared.