Before a natural sound can be recognized, an auditory signature of its source must be learned through experience. Here we used random waveforms to probe the formation of new memories for arbitrary complex sounds. A behavioral measure was designed, based on the detection of repetitions embedded in noises up to 4 s long. Unbeknownst to listeners, some noise samples reoccurred randomly throughout an experimental block. Results showed that repeated exposure induced learning for otherwise totally unpredictable and meaningless sounds. The learning was unsupervised and resilient to interference from other task-relevant noises. When memories were formed, they emerged rapidly, performance became abruptly near-perfect, and multiple noises were remembered for several weeks. The acoustic transformations to which recall was tolerant suggest that the learned features were local in time. We propose that rapid sensory plasticity could explain how the auditory brain creates useful memories from the ever-changing, but sometimes repeating, acoustical world.