Role of denoising the age–metallicity relation in recovering the metallicity gradient from the scatter in [Fe/H] as a function of age. The age–metallicity relation for g2.79e12 (gray scale) with 15% age and 0.05 dex [Fe/H] uncertainty added (blue scale) is shown in the top panel. The horizontal lines correspond to the upper and lower bounds used to calculate Range [Fe/H] (age) measured with (blue) and without (white) measurement uncertainties. The range measured using the data with uncertainties is much larger than the range measured using the true age and [Fe/H] values for age >9 Gyr. The middle panel shows the distribution of the denoised ages (Section 3.2) and [Fe/H] (plasma) match well the age–metallicity relation of the true distribution. The presence of present day observational uncertainties (also shown in the bottom panel) makes denoising the age–metallicity relation a requirement to recover the structure in this plane, and thus Range [Fe/H] (age).