We show that for any noisy quantum channel, there always exists a coherent control procedure that allows one to filter, i.e., probabilistically obtain, a noiseless channel, i.e., unitary. Such a perfect error filtration is achieved in the limit of the coherent control of infinitely many copies of the channel, possibly and rather counterintuitively, after the injection of additional noise. We provide the necessary and sufficient condition for filtering, we estimate the optimal probability and we show that error filtration is applicable to a channel if a decoding operation is allowed on the receiver’s side and that the optimal decoding is efficiently computable. Finally, we demonstrate that the principle of perfect error filtration can be applied in the circuit model that provides the practical application of our result for a broad application of quantum information.