The Paradox of Steady-State Light Diffusion.

For over thirty years, the definition of the diffusion coefficient in light transport has been the subject of persistent debate. Its canonical expression includes an explicit dependence on absorption, violating a fundamental scaling property of the radiative transfer equation (RTE). In the time domain (TD), evidence shows that the correct definition is independent of absorption, yet absorption-dependent formulations unfortunately remain common in practical data analysis. In the continuous-wave regime, the radial decay of the RTE can be reproduced by an absorption-dependent coefficient, but this does not imply that steady-state transport is genuinely diffusive. Here, this controversy is resolved through an exact consistency test based solely on the requirement that diffusion converges to the RTE in the limit of infinite propagation. In the TD, we prove that the absorption-independent coefficient is both necessary and sufficient for exact long-time convergence. In the continuous-wave regime, we prove analytically that no scalar diffusion coefficient can make diffusion asymptotically equivalent to the RTE when absorption is nonzero: matching the dominant attenuation length fixes one coefficient, whereas matching the residue requires a different one. We further show that this failure is not caused by any finite set of ballistic or few-scattering contributions, and quantify the intrinsic error introduced by incorrect parameterizations in idealized absorption-retrieval scenarios. These results establish the time-domain formulation as the only self-consistent reference and call for a re-examination of how diffusion is applied in optical transport studies.