The concept that catalytic enzymes can act as molecular machines transducing chemical activity into motion has conceptual and experimental support, but experimental support has involved oligomeric enzymes, often studied under conditions where the substrate concentration is higher than biologically relevant and accordingly exceeds k(M), the Michaelis constant. Urease, a hexamer of subunits, has been considered to be the gold standard demonstrating enhanced diffusion. Here we show that urease and certain other oligomeric enzymes dissociate above k(M) into their subunits that diffuse more rapidly, thus providing a simple physical mechanism that contributes to enhanced diffusion in this regime of concentrations. Mindful that this conclusion may be controversial, our findings are supported by four independent analytical techniques: static light scattering, dynamic light scattering (DLS), size-exclusion chromatography (SEC), and fluorescence correlation spectroscopy (FCS). Data for urease are emphasized and the conclusion is validated for hexokinase, acetylcholinesterase, and aldolase. For hexokinase and aldolase no enhanced diffusion is observed except under conditions when these oligomeric enzymes dissociate. At substrate concentration regimes below k(M) at which acetylcholinesterase and urease do not dissociate, our finding showing up to 10% enhancement of the diffusion coefficient is consistent with various theoretical scenarios in the literature.