Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the assocaited double Edelman– Greene coefficients, the double Schur expansion of these functions, are positive, a result later refined by Anderson. They further asked for a combinatorial proof of this positivity. We provide the first such proof, together with a combinatorial formula that manifests the finer positivity established by Anderson. Our formula is built from two combinatorial models: bumpless pipedreams and increasing chains in the Bruhat order. The proof relies on three key ingredients: a correspondence between these two models, a natural subdivision of bumpless pipedreams, and a symmetry property of increasing chains. This talk is based on joint work with Jack Chou.