Can we map the channels at one set of antennas and one frequency band to the channels at another set of antennas-possibly at a different location and a different frequency band If this channel-to-channel mapping is possible, we can expect dramatic gains for massive MIMO systems. For example, in FDD massive MIMO, the uplink channels can be mapped to the downlink channels or the downlink channels at one subset of antennas can be mapped to the downlink channels at all the other antennas. This can significantly reduce (or even eliminate) the downlink training/feedback overhead. In the context of cell-free/distributed massive MIMO systems, this channel mapping can be leveraged to reduce the fronthaul signaling overheadIn this paper, we introduce the new concept of channel mapping in space and frequency, where the channels at one set of antennas and one frequency band are mapped to the channels at another set of antennas and frequency band. First, we prove that this channel-to-channel mapping function exists under certain conditions. Then, we leverage the powerful learning capabilities of deep neural networks to efficiently learn this non-trivial channel mapping function, which is also confirmed by the simulation results.