However, this picture suggests to me that recessions follow periods of higher inflation, and maybe where that inflation continues during the recession, it could be put down to a sort of residual momentum. Why should prices fall at precisely the moment the NBER says a recession has started? Even a cut flower will maintain its bloom for a while.
On the other hand, it seems clear from the above graph that prices do generally seem to fall after a recession. Perhaps this is because of the recently reinforced lesson about thrift, so people become less keen to spend too much on stuff they don't need.
But it's also possible that the recession has cleansed certain inefficiencies in the use of capital - businesses that should have folded faster - and as that capital gets better employed elsewhere, it does its work of improving productivity.
Which it needs to, when people have become more cost-conscious. I recall reading about an American who found a way to sell dresses for a dollar in the Great Depression - he used a machine to stamp out the outline of 100 at a time, so only the machine sewing was needed, not the measuring and cutting. So it was still possible to buy a dress for your sweetheart when money was tight.
But the little hand-mill of monetary inflation continues to grind...