  Static disorder in a 3D crystal degrades the ideal ballistic dynamics until
it produces a localized regime. This Metal-Insulator Transition is often
preceded by coherent diffusion. By studying three paradigmatic 1D models,
namely the Harper-Hofstadter-Aubry-Andr\'e and Fibonacci tight-binding chains,
along with the power-banded random matrix model, we show that whenever coherent
diffusion is present, transport is exceptionally stable against decoherent
noise. This is completely at odds with what happens for coherently ballistic
and localized dynamics, where the diffusion coefficient strongly depends on the
environmental decoherence. A universal dependence of the diffusion coefficient
on the decoherence strength is analytically derived: the diffusion coefficient
remains almost decoherence-independent until the coherence time becomes
comparable with the mean elastic scattering time.
  Thus, systems with a quantum diffusive regime could be used to design robust
quantum wires. Moreover our results might shed new light on the functionality
of many biological systems, which often operate at the border between the
ballistic and localized regimes.
