QuadriFlow is a scalable algorithm for generating quadrilateral surface meshes based on the Instant Field-Aligned Meshes. Our algorithm efficiently produces meshes with many fewer singularities. Singularities in quadrilateral meshes cause problems for many applications, including parametrization and rendering with Catmull-Clark subdivision surfaces. Local optimization algorithms usually produce meshes with many singularities, whereas the best algorithms tend to require non-local optimization, and therefore are slow. We propose an efficient method to minimize singularities by combining the Instant Meshes objective with a system of linear and quadratic constraints, which are enforced by solving a global minimum-cost network flow problem and local boolean satisfiability problems. We have verified the robustness and efficiency of our method on a 17791 3D objects in the wild. Our evaluation shows that the quality of the quadrangulations generated by our method is as good as, if not better than, those from other methods, achieving about four times fewer singularities than Instant Meshes.