How can I get a TaskScheduler for a Dispatcher?

I've got an application with multiple Dispatchers (aka GUI threads, aka message pumps) to ensure that a slow, unresponsive portion of the GUI runs without affecting the rest of the application too heavily. I also use Task a lot.

Currently I've got code that conditionally runs an Action on a TaskScheduler or a Dispatcher and then returns a Task either directly or by manually creating one using TaskCompletionSource. However, this split personality design makes dealing with cancellation, exceptions etc. all much more complicated than I'd like. I want to use Tasks everywhere and DispatcherOperations nowhere. To do that I need to schedule tasks on dispatchers - but how?

How can I get a TaskScheduler for any given Dispatcher?

Edit: After the discussion below, I settled on the following implementation:

public static Task<TaskScheduler> GetScheduler(Dispatcher d) {
    var schedulerResult = new TaskCompletionSource<TaskScheduler>();
    d.BeginInvoke(() => 
        schedulerResult.SetResult(
            TaskScheduler.FromCurrentSynchronizationContext()));
    return schedulerResult.Task;
}