The influence of the biofilm matrix on molecular diffusion is commonly hypothesized to be responsible for emergent characteristics of biofilms such as nutrient trapping, signal accumulation and antibiotic tolerance. Hence quantifying the molecular diffusion coefficient is important to determine whether there is an influence of biofilm microenvironment on the mobility of molecules. Here, we use single plane illumination microscopy fluorescence correlation spectroscopy (SPIM-FCS) to obtain 3D diffusion coefficient maps with micrometre spatial and millisecond temporal resolution of entire Pseudomonas aeruginosa microcolonies. We probed how molecular properties such as size and charge as well as biofilm properties such as microcolony size and depth influence diffusion of fluorescently labelled dextrans inside biofilms. The 2 MDa dextran showed uneven penetration and a reduction in diffusion coefficient suggesting that the biofilm acts as a molecular sieve. Its diffusion coefficient was negatively correlated with the size of the microcolony. Positively charged dextran molecules and positively charged antibiotic tobramycin preferentially partitioned into the biofilm and remained mobile inside the microcolony, albeit with a reduced diffusion coefficient. Lastly, we measured changes of diffusion upon induction of dispersal and detected an increase in diffusion coefficient inside the biofilm before any loss of biomass. Thus, the change in diffusion is a proxy to detect early stages of dispersal. Our work shows that 3D diffusion maps are very sensitive to physiological changes in biofilms, viz. dispersal. However, this study also shows that diffusion, as mediated by the biofilm matrix, does not account for the high level of antibiotic tolerance associated with biofilms.