Most of Earth's volcanoes are under water. As a result of their relative inaccessibility, little is known of the structure and evolution of submarine volcanoes. Advances in navigation and sonar imaging techniques have made it possible to map submarine volcanoes in detail, and repeat surveys allow the identification of regions where the depth of the sea floor is actively changing. Here we report the results of a bathymetric survey of Monowai submarine volcano in the Tonga-Kermadec Arc, which we mapped twice within 14 days. We found marked differences in bathymetry between the two surveys, including an increase in seafloor depth up to 18.8 m and a decrease in depth up to 71.9 m. We attribute the depth increase to collapse of the volcano summit region and the decrease to growth of new lava cones and debris flows. Hydroacoustic T-wave data reveal a 5-day-long swarm of seismic events with unusually high amplitude between the surveys, which directly link the depth changes to explosive activity at the volcano. The collapse and growth rates implied by our data are extremely high, compared with measured long-term growth rates of the volcano, demonstrating the pulsating nature of submarine volcanism and highlighting the dynamic nature of the sea floor.