How can we do that with Guava? Notice the presence of List<K> in the return type since many keys can map to the same value in any normal map.
public static <K, V> Map<V, List<K>> inverse(Map<K, V> map){
    Map<V, List<K>> result = new LinkedHashMap<V, List<K>>();
    for (Map.Entry<K, V> entry : map.entrySet()) {
        if(!result.containsKey(entry.getValue())){
            result.put(entry.getValue(), new ArrayList<K>());                
        }
        result.get(entry.getValue()).add(entry.getKey());
    }        
    return result;        
}
BiMap seems to insist on the unicity of the values, but I don't have this luxury.