We consider approximate inference in Gaussian probabilistic models with approximate free energy methods. We define the (fractional) Bethe free energy and directly minimize it. A lower bound for the free energies is derived and we give necessary conditions for the fractional Bethe free energy to be bounded. Our results are in line with the earlier work on the analysis of standard message passing done by Malioutov et al.2006 and Weiss and Freeman 2001, and improve on them by showing that if pairwise normalizability does not hold standard message passing is guaranteed to converge to a global minimum only in special cases. Joint work with Tom Heskes.