Imaging single proteins or RNAs allows direct visualization of the inner workings of the cell. Typically, three-dimensional (3D) images are acquired by sequentially capturing a series of 2D sections. The time required to step through the sample often impedes imaging of large numbers of rapidly moving molecules. Here we applied multifocus microscopy (MFM) to instantaneously capture 3D single-molecule real-time images in live cells, visualizing cell nuclei at 10 volumes per second. We developed image analysis techniques to analyze messenger RNA (mRNA) diffusion in the entire volume of the nucleus. Combining MFM with precise registration between fluorescently labeled mRNA, nuclear pore complexes, and chromatin, we obtained globally optimal image alignment within 80-nm precision using transformation models. We show that beta-actin mRNAs freely access the entire nucleus and fewer than 60% of mRNAs are more than 0.5 microm away from a nuclear pore, and we do so for the first time accounting for spatial inhomogeneity of nuclear organization.