  A photonic circuit is generally described as a structure in which light
propagates by unitary exchange and transfers reversibly between channels. In
contrast, the term `diffusive' is more akin to a chaotic propagation in
scattering media, where light is driven out of coherence towards a thermal
mixture. Based on the dynamics of open quantum systems, the combination of
these two opposites can result in novel techniques for coherent light control.
The crucial feature of these photonic structures is dissipative coupling
between modes, via an interaction with a common reservoir. Here, we demonstrate
experimentally that such systems can perform optical equalisation to smooth
multimode light, or act as a distributor, guiding it into selected channels.
Quantum thermodynamically, these systems can act as catalytic coherent
reservoirs by performing perfect non-Landauer erasure. For lattice structures,
localised stationary states can be supported in the continuum, similar to
compacton-like states in conventional flat band lattices.
