  We present a summary of the flavor composition measurements for the diffuse
astrophysical neutrino flux using data from the IceCube Neutrino Observatory at
the South Pole. IceCube has identified candidate astrophysical tau neutrinos
through two different approaches. One approach used a dedicated particle
identification algorithm for the classification and reconstruction of the
'Double Cascade' event topology, a signature of tau neutrino charged current
interactions. This first approach is applied to the High Energy Starting Events
(HESE) sample, an all-sky, all-flavor set of neutrino events with energy above
60~TeV encompassing 12 years of IceCube livetime. We show that the addition of
more years of data and updated ice properties on the HESE sample delivers
tighter constraints on the flavor composition of the astrophysical neutrino
flux than previous IceCube analyses, in particular when it is fit in
combination with high statistics samples of through-going tracks and cascades.
A second approach uses a sensitive machine-learning-based selection technique
that finds seven candidate events in 9.7 years of IceCube data. This approach
excludes the zero astrophysical tau neutrino hypothesis at the highest
statistical significance to date.
