Can you declare a Java enum to have variable generic types per instance?

Question

What I am trying to do is implement a fixed set of converters as abstract enums with individual implementations, and supply different generics per implementation. The below code doesn't work, but it should indicate what I am trying to do. I am all but certain the answer is 'no'. If I remove all generics and use type casting, this will for sure work. But I'd prefer generics

    public enum Converter implements ValueConverter<I,O> {
        LONG_DOUBLE<Long,Double> {
            @Override
            public Long convertInput(Double value) {
                return null;
            }

            @Override
            public Double convertOutput(Long value) {
                return null;
            }
        },
        DATE_LOCALDATE<Date,LocalDate> {
            @Override
            public Date convertInput(LocalDate value) {
                return null;
            }

            @Override
            public LocalDate convertOutput(Date value) {
                return null;
            }
        }
    }