Perfectly diffuse wave fields are the underlying assumption for noise-correlation tomography in seismology, nondestructive testing, and elastography; however, perfectly diffuse fields are rarely encountered in real-world applications. We show that homogeneously distributed magnetic microparticles allow instantaneous generation of a diffuse wave field, which can be imaged using a clinical probe connected to a fully programmable ultrasound scanner. The particles are placed inside a bilayered hydrogel and act as elastic-wave sources on excitation by a magnetic pulse. Using ultrafast ultrasound imaging coupled to phase tracking, the diffuse elastic wave field is imaged. This allows the local wave velocity to be measured everywhere on the image using noise-correlation algorithms inspired by seismology. Thanks to this instantaneous diffuse wave field, a very short acquisition time is sufficient to retrieve the wave speed contrast of a bilayered phantom. The correlation time window can be shrunk down to three time samples, which we show in a numerical simulation mimicking the experimental conditions. Our experimental and numerical results are consistent with theoretical predictions made by information theory, and they pave the way for real-time elasticity imaging. This is of particular interest for monitoring of medical treatments through real-time tissue-elasticity assessment, and it is also applicable in related fields such as seismology and nondestructive testing.