An important goal in chemistry is to prepare compounds with unusual oxidation states showing exciting properties. For gold (Au), the relativistic expansion of its 5d orbitals makes it form high oxidation state compounds. Thus far, the highest oxidation state of Au known is +5. Here, we propose high pressure as a controllable method for preparing +4 and +6 oxidation states in Au via its reaction with fluorine. First-principles swarm-intelligence structure search identifies two hitherto unknown stoichiometric compounds, AuF4 and AuF6, exhibiting typical molecular crystal character. The high-pressure phase diagram of Au fluorides is rather different from Cu or Ag fluorides, which is indicated by stable chemical compositions and the pressures needed for the synthesis of these compounds. This difference can be associated with the stronger relativistic effects in Au relative to Cu or Ag. Our work represents a significant step forward in a more complete understanding of the oxidation states of Au.