Diffusive lossless energy and coherence transfer by noisy coupling

Here we show that noisy coupling can lead to diffusive lossless energy transfer between individual quantum systems retaining a quantum character leading to entangled stationary states. Coherence might flow diffusively while being summarily preserved even when energy exchange is absent. Diffusive dynamics persists even in the case when additional noise suppresses all the unitary excitation exchange: arbitrarily strong local dephasing, while destroying quantum correlations, is not affecting energy transfer.