Many applications that involve laser sources suffer from undesired coherent artifacts, such as speckle noise. The speckle noise is typically suppressed by superimposing many uncorrelated speckle realizations and summing their intensities incoherently. Unfortunately, it is difficult to accumulate a large number of independent speckle realizations on short time scales. Here we propose and demonstrate a new spatio-temporal mechanism for rapid speckle suppression in a highly multimode laser source. We show that in the regime of short time scales, the spatial coherence (and therefore speckle contrast) depends on the number of longitudinal modes, even for thin diffusers and lasers with limited spectral bandwidth. This counter-intuitive result is explained by an interplay between longitudinal and transverse laser modes. The new spatio-temporal mechanism is demonstrated for rapid speckle-free imaging of a fast moving object.