In the present study, we have examined the diffraction of detonation in weakly unstable hydrogen–oxygen–argon mixtures. High accuracy and computational efficiency are obtained using a high-order WENO scheme together with adaptive mesh refinement, which enables handling realistic geometries with resolution at the micrometer level. Both detailed chemistry and spectroscopic models of laser induced fluorescence and chemiluminescence were included to enable a direct comparison with experimental data. Agreement was found between the experiments and the simulations in terms of detonation diffraction structure both for sub-critical and super-critical regimes. The predicted wall reflection distance is about 12–14 cell widths, in accordance with previous experimental studies. Computations show that the re-initiation distance is relatively constant, at about 12–15 cell widths, slightly above the experimental value of 11 cell widths. The predicted critical channel height is 10–11 cell widths, which differs from experiments in circular tubes but is consistent with rectangular channel results.