We introduce Daguerro, a strategy for learning directed acyclic graphs (DAGs). In contrast to previous methods, our problem formulation (i) guarantees to learn a DAG, (ii) does not propagate errors over multiple stages, and (iii) can be trained end-to-end without pre-processing steps. Our algorithm leverages advances in differentiable sparse structured inference for learning a total ordering of the variables in the simplex of permutation vectors (the permutahedron), allowing for a substantial reduction in memory and time complexities w.r.t. existing permutation-based continuous optimization methods.