The recently introduced random purification channel, which converts 𝑛 copies of an arbitrary mixed quantum state into 𝑛 copies of the same uniformly random purification, has emerged as a powerful tool in quantum information theory. We give a remarkably simple construction of this channel, making its known properties — and several new ones — immediately transparent. We also introduce a channel-level analogue, which we call the random Stinespring superchannel. This consists in a procedure to transform 𝑛 parallel queries of an arbitrary quantum channel into 𝑛 parallel queries of the same uniformly random Stinespring isometry, via universal encoding and decoding operations that are efficiently implementable. Throughout the presentation, we are going to discuss some surprising applications in quantum learning theory and quantum Shannon theory.