Microscopic pathways of structural phase transitions inmetal halide perovskites are difficult to probe because they occur over disparate time and length scales and because electron-based microscopies typically used to directly probe nanoscale dynamics of phase transitions often damage metal halide perovskite materials. Using in situ nanoscale cathodoluminescence microscopy with low electron beam exposure, we visualize nucleation and growth in the thermally driven transition to the perovskite phase in hundreds of non-perovskite phase nanowires. In combination with molecular dynamics simulations, we reveal that the transformation does not follow a simple martensitic mechanism, but proceeds despite a substantial energy barrier via ion diffusion through a liquid-like interface between the two structures. While cations are disordered in this liquid-like region, the halide ions retain substantial spatial correlations. This detailed picture not only reveals how phase transitions between disparate structures can proceed, but also opens the possibility to control such processes.