Recent theories predicted that $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$ is a higher-order topological insulator (HOTI) exhibiting one-dimensional (1D) conducting edge states, and that ${\mathrm{T}}_{d}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$ becomes a HOTI with broken inversion symmetry under strain or lattice distortion. Here, we report the transport evidence for 1D helical edge states in ${\mathrm{MoTe}}_{2}$ thin flakes. Under an in-plane magnetic field perpendicular to the current, Altshuler-Aronov-Spivak interference of edge states is observed, in which the oscillating period corresponding to magnetic flux $h/2e$ agrees with the lateral cross-sectional area. The absence of Aharonov-Bohm interference stems from the helical nature of the edge states. Temperature evolution of the fast Fourier transform amplitude is further obtained, indicating the quasiballistic transport mode. Our work deepens the understanding of higher-order topological properties of ${\mathrm{MoTe}}_{2}$, paving the way for further topological electronics.