  Optical spectra contain a wealth of information about the physical properties
and formation histories of galaxies. Often though, spectra are too noisy for
this information to be accurately retrieved. In this study, we explore how
machine learning methods can be used to de-noise spectra and increase the
amount of information we can gain without having to turn to sample averaging
methods such as spectral stacking. Using machine learning methods trained on
noise-added spectra - SDSS spectra with Gaussian noise added - we investigate
methods of maximising the information we can gain from these spectra, in
particular from emission lines, such that more detailed analysis can be
performed. We produce a variational autoencoder (VAE) model, and apply it on a
sample of noise-added spectra. Compared to the flux measured in the original
SDSS spectra, the model values are accurate within 0.3-0.5 dex, depending on
the specific spectral line and S/N. Overall, the VAE performs better than a
principle component analysis (PCA) method, in terms of reconstruction loss and
accuracy of the recovered line fluxes. To demonstrate the applicability and
usefulness of the method in the context of large optical spectroscopy surveys,
we simulate a population of spectra with noise similar to that in galaxies at
$z = 0.1$ observed by the Dark Energy Spectroscopic Instrument (DESI). We show
that we can recover the shape and scatter of the MZR in this "DESI-like"
sample, in a way that is not possible without the VAE-assisted de-noising.
