<p>The QCD axion in the pre-inflation scenario faces a stringent isocurvature constraint, which requires a relatively low Hubble scale during inflation. If the axion was heavier than the Hubble scale during inflation, its isocurvature is suppressed and the constraint disappears. We point out a novel mechanism for achieving this, relying on the topological nature of a BF-type (monodromy) mass for the axion. Such a mass term has an integer coefficient, so it could naturally have been very large during inflation and exactly zero by the time of the QCD phase transition. This integer can be viewed as a quantized flux, which is discharged in a first-order phase transition that proceeds by the nucleation of charged branes. This mechanism can be embedded in cosmology in several different ways, with tunneling during, at the end of, or after inflation. We provide a detailed case study of the scenario in which the tunneling event occurs during inflation. We also comment briefly on possible UV completions within extra-dimensional gauge theories and string theory. Intriguingly, the phase transition could be accompanied by the emergence of the chiral Standard Model field content from a non-chiral theory during inflation.</p>