We used a new quantitative high spatiotemporal resolution phase imaging tool to explore the nuclear structure and dynamics of individual cells. We used a novel analysis tool to quantify the diffusion outside and inside the nucleus of live cells. We also obtained information about the nuclear spatio temporal mass density in metastatic cells. The results indicate that in the cytoplasm, the intracellular transport is mainly active (direct, deterministic), while inside the nucleus it is both active and passive (diffusive, random). We calculated the standard deviation of velocities in active transport and the diffusion coefficient for passive transport.