Ability to recover ∇[Fe/H](τ) from Range[Fe/H](age) in g2.79e12 without any observational errors added (left panel). The middle panel is the same as the left panel but with 15% age and 0.05 dex[Fe/H] uncertainties added. The range becomes artificially high at older ages past the knee in the age–metallicity relation due to present day age errors. The recovery of ∇[Fe/H](τ) using the denoised age-metallicity relation is given in the right panel. The comparison between denoising the data and the truth (left panel) is strikingly similar.