  The guiding and transport of energy, for example of electromagnetic waves
underpins many technologies that have shaped modern society, ranging from long
distance optical fibre telecommunications to on-chip optical processors.
Traditionally, a mechanism is required that exponentially localises the waves
or particles in the confinement region, e.g. total internal reflection at a
boundary. We introduce a waveguiding mechanism that relies on a different
origin for the exponential confinement and that arises due to the physics of
diffusion. We demonstrate this concept using light and show that photon density
waves can propagate as a guided mode along a core-structure embedded in a
scattering, opaque material, enhancing light transmission by orders of
magnitude and along non-trivial, e.g. curved trajectories. This waveguiding
mechanism can also occur naturally, for example in the cerebral spinal fluid
surrounding the brain, along tendons in the human body and is to be expected in
other systems that follow the same physics e.g. neutron diffusion.
