You can do this:
Map<K, V> map = ...;
ListMultimap<V, K> inverse = Multimaps.invertFrom(Multimaps.forMap(map),
ArrayListMultimap.<V,K>create());
Do note that pretty much any time you write Map<K, List<V>>
or Map<K, Set<V>>
or some such, a ListMultimap<K, V>
or SetMultimap<K, V>
is what you really want.