In this talk, we provide characterizations on the Gromov-Hausdorff stability to a flat torus from a closed Riemannian manifold with Ricci and integral scalar curvature bounds, in terms of harmonic maps and harmonic $1$-forms. Applications include a new topological stability result to a flat torus. This is a joint work with C. Ketterer, I. Mondello, R. Perales and C. Rigoni.