How free are graduate students to choose research topics given their department?

I'm sort of foggy in general about how this works. If you are, say a a computer science graduate student, what kind of freedom do you have to pick a research topic that focuses more on something like cellular biology, swarms, or string theory? Do you need to change departments? Do you need to illustrate some connection back to CS techniques? Do you just have to pursuade your advisor to issue a blessing?