  We report the discovery and validation of two TESS exoplanets orbiting faint
M dwarfs: TOI-4479b and TOI-2081b. We have jointly analyzed space (TESS
mission) and ground based (MuSCAT2, MuSCAT3 and SINISTRO instruments)
lightcurves using our multi-color photometry transit analysis pipeline. This
allowed us to compute contamination limits for both candidates and validate
them as planet-sized companions. We found TOI-4479b to be a sub-Neptune-sized
planet ($R_{p}=2.82^{+0.65}_{-0.63}~\rm R_{\oplus}$) and TOI-2081b to be a
super-Earth-sized planet ($R_{p}=2.04^{+0.50}_{-0.54}~\rm R_{\oplus}$).
Furthermore, we obtained that TOI-4479b, with a short orbital period of
$1.15890^{+0.00002}_{-0.00001}~\rm days$, lies within the Neptune desert and is
in fact the largest nearly ultra-short period planet around an M dwarf known to
date. These results make TOI-4479b rare among the currently known exoplanet
population around M dwarf stars, and an especially interesting target for
spectroscopic follow-up and future studies of planet formation and evolution.
