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Certain quantum devices, such as half-wave plates and quarter-wave plates in quantum optics, are bidirectional, meaning that the roles of their input and output ports can be exchanged. Bidirectional devices can be used in a forward mode and a backward mode, corresponding to two opposite choices of the input-output direction. They can also be used in a coherent superposition of the forward and backward modes, giving rise to new operations with indefinite input-output direction. In this work we explore the potential of input-output indefiniteness for the transfer of classical and quantum information through noisy channels. We first formulate a model of communication from a sender to a receiver via a noisy channel used in indefinite input-output direction. Then, we show that indefiniteness of the input-output direction yields advantages over standard communication protocols in which the given noisy channel is used in a fixed input-output direction. These advantages range from a general reduction of noise in bidirectional processes, to heralded noiseless transmission of quantum states, and, in some special cases, to a complete noise removal. The noise reduction due to input-output indefiniteness can be experimentally demonstrated with current photonic technologies, providing a way to investigate the operational consequences of exotic scenarios characterised by coherent quantum superpositions of forward-time and backward-time processes.