Pulsed cavitation ultrasound therapy (PCUT) is an effective non-invasive therapeutic approach in various medical indications that relies on the mechanical effects generated by cavitation bubbles. Even though limited by the poor contrast, conventional ultrasound B-Mode imaging has been widely used for the guidance and monitoring of the therapeutic procedure, allowing the visualization of the cavitation bubble cloud. However, the visualization of the bubble cloud is often limited in deep organs such as the liver and the heart and remains moreover completely subjective for the operator. Our goal is to develop a new imaging mode to better identify the cavitation cloud. Active and passive cavitation imaging methods have been developed but none of them has been able to locate the cavitation bubble created by PCUT in real-time and in moving organs. In this paper we propose a passive ultrasound imaging approach combined with a spatiotemporal singular value decomposition filter to detect and map the bubble cloud with high sensitivity and high contrast. In moving applications at a maximal motion speed of 10 mm s-1, the contrast-to-noise ratio for passive cavitation imaging is up to 10 times higher than for active cavitation imaging, with a temporal resolution of about 100 ms. The mapping of the bubble cloud can be overlaid in real-time to the conventional B-Mode, which permits to locate the cavitation phenomena in relation to the anatomic image. Finally, we extend the technique to volumetric imaging and show its feasibility on moving phantoms.