We present observations of rapid (sub-second) optical flux variability in V404 Cyg during its 2015 June outburst. Simultaneous three-band observations with the ULTRACAM fast imager on four nights show steep power spectra dominated by slow variations on ~100-1000s timescales. Near the peak of the outburst on June 26, a dramatic change occurs and additional, persistent sub-second optical flaring appears close in time to giant radio and X-ray flaring. The flares reach peak optical luminosities of ~few x 10^{36} erg/s. Some are unresolved down to a time resolution of 24 milliseconds. Whereas the fast flares are stronger in the red, the slow variations are bluer when brighter. The redder slopes, emitted power, and characteristic timescales of the fast flares can be explained as optically-thin synchrotron emission from a compact jet arising on size scales ~140-500 Gravitational radii (with a possible additional contribution by a thermal particle distribution). The origin of the slower variations is unclear. The optical continuum spectral slopes are strongly affected by dereddening uncertainties and contamination by strong H{alpha} emission, but the variations of these slopes follow relatively stable loci as a function of flux. Cross-correlating the slow variations between the different bands shows asymmetries on all nights consistent with a small red skew (i.e., red lag). X-ray reprocessing and non-thermal emission could both contribute to these. These data reveal a complex mix of components over five decades in timescale during the outburst.
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