  We consider a system of $N$ parallel queues with identical exponential
service rates and a single dispatcher where tasks arrive as a Poisson process.
When a task arrives, the dispatcher always assigns it to an idle server, if
there is any, and to a server with the shortest queue among $d$ randomly
selected servers otherwise $(1 \leq d \leq N)$. This load balancing scheme
subsumes the so-called Join-the-Idle Queue (JIQ) policy $(d = 1)$ and the
celebrated Join-the-Shortest Queue (JSQ) policy $(d = N)$ as two crucial
special cases. We develop a stochastic coupling construction to obtain the
diffusion limit of the queue process in the Halfin-Whitt heavy-traffic regime,
and establish that it does not depend on the value of $d$, implying that
assigning tasks to idle servers is sufficient for diffusion level optimality.
