An ideal invisibility cloak makes any object within itself indistinguishable from its surrounding—for all colors, directions, and polarizations of light. Nearly ideal cloaks have recently been realized for turbid light-scattering media under continuous-wave illumination. Here, we ask whether these cloaks also work under pulsed illumination. Our time-resolved imaging experiments on simple core–shell cloaks show that they do not: they appear bright with respect to their surrounding at early times and dark at later times, leading to vanishing image contrast for time-averaged detection. Furthermore, we show that the same holds true for more complex cloaking architectures designed by spatial coordinate transformations. We discuss implications for diffuse optical tomography and possible applications in terms of high-end security features.