The 2018 Kīlauea caldera collapse produced extraordinary sequences of seismicity and deformation, with 62 episodic collapse events which significantly altered the landscape of the summit region. Despite decades of focused scientific studies at Kīlauea, detailed information about the internal structure of the volcano is limited. Recently developed techniques in seismic interferometry can be used to monitor the internal structure of an active volcano more directly by detecting subtle spatiotemporal changes in seismic wave velocity, but their utility relies on accurate interpretations of the underlying phenomena causing those velocity changes. Here, we retrospectively apply repeating-earthquake-based seismic interferometry to the 2018 Kīlauea eruption sequence. We find that seismic velocities changed over two distinct time scales: a sudden increase followed by a slower decrease in velocity in the hours following each collapse event, and a gradual, long-term decrease in velocity over several weeks that ceased approximately 1 month prior to the end of the eruption. Modeling suggests that short-term changes can be explained by magma reservoir pressurization which specifically closed vertical ring fractures. Long-term changes are related to subsidence of the caldera and likely include the influence of inelastic strain from the formation of new fractures. These observations provide new insights into the evolution of Kīlauea during its progressive collapse and will inform future interpretations for near-real-time monitoring at hazardous volcanoes around the world using similar techniques, especially where a dominant fracture orientation is present.