Swarms make a return in Pokémon Brilliant Diamond & Shining Pearl. When you have obtained the National Pokédex, speak to Dawn/Lucas in Sandgem Town and they'll recommend talking to their sister. If you do, then she will tell you she saw that a swarm of Pokémon was happening.
These Pokémon are all outside the Sinnoh Pokédex and can only be found here or the Grand Underground. The Pokémon that spawns changes each day.
After the first swarm is told to you by Dawn/Lucas' sister, you will be able to see what the Swarm is through the pause menu in the game which will lead you to the map. When you go into the area which has the Swarm, the Pokémon will rapidly pop out of the overworld grass and can be interacted with there.