Polymer foams comprising macropores, the macropores having average cross sections of above 500 nm, are obtainable by reacting one or more epoxy resins with one or more amphiphilic epoxy resin hardeners in water in a phase inversion polymerization, where, during the phase inversion polymerization, but after phase inversion has taken place, a volume increase of the internal voids which form initially, and which are present predominantly as micropores having average cross sections of below 500 nm, is induced such that the fraction of the macropores—relative to the entirety of micropores and macropores present in the polymer foam—at the end of the phase inversion polymerization is above 50% by volume. Polymer foams of the present invention are suitable for use as acoustic insulation materials in means of transport and in industrial and plant construction.