  We establish short-time existence and regularity for higher-order flows
generated by a class of polynomial natural tensors that, after an adjustment by
the Lie derivative of the metric with respect to a suitable vector field, have
strongly parabolic linearizations. We apply this theorem to flows by powers of
the Laplacian of the Ricci tensor, and to flows generated by the ambient
obstruction tensor. As a special case, we prove short-time existence for a type
of Bach flow.
