Higher costs for any inputs, not just wages, can drive it as well, no? Even if spending remains flat, that is, prices go up and people just buy less stuff while spending about the same amount of money, or even spending less?
If input costs like energy go up, which affect virtually every item, then that can lead to higher inflation because the aggregate spending across everything can't drop.
[EDIT] that is, yes, falling spending would have a "cooling" effect, but if costs for, say, productive land, go up fast enough, you can still see inflation in the face of falling spending.