Observation of random, nonrepetitive phenomena is of critical importance in astronomy, spectroscopy, biology, and remote sensing. Heralded by weak signals, hidden in noise, they pose basic detection challenges. In contrast to repetitive waveforms, a single-instance signal cannot be separated from noise through averaging. Here, we show that a fast, randomly occurring event can be detected and extracted from a noisy background without conventional averaging. An isolated 80-picosecond pulse was received with confidence level exceeding 99%, even when accompanied by noise. Our detector relies on instantaneous spectral cloning and a single-step, coherent field processor. The ability to extract fast, subnoise events is expected to increase detection sensitivity in multiple disciplines. Additionally, the new spectral-cloning receiver can potentially intercept communication signals that are presently considered secure.