Branching, yes. As a species population grows, portions of it become isolated from other portions (through distance, intervening geography, etc.), and the lack of interbreeding allows each subpopulation to evolve off in its own direction, resulting in two or more different species where once there was only one.
This is no different than how we ended up with dozens of new breeds of dogs, from a much less diverse original stock -- different descendant lineages went their separate ways. The entire dog population didn't have to change together in only one way. Likewise for how we now have hundreds of varieties of roses, while the wild rose still continues to exist.
But the cool thing is, you don't just get intra-species diversity; e.g., Rottweilers and Cocker Spaniels, you get inter-species diversity; e.g., whales and hippos.