Here's how:
1. Obtain a Nintendo 3DS or New Nintendo 3DS.
2. Download and install the Pokémon Bank application on your 3DS.
3. Transfer your Pokémon from Diamond to Black/White or Black 2/White 2. You can do this by using the Poké Transporter feature in those games.
4. Transfer your Pokémon from Black/White or Black 2/White 2 to the Pokémon Bank using the same method you used to transfer them from Diamond.
5. Download and install the Pokémon Bank app on your Nintendo Switch.
6. Transfer your Pokémon from the Pokémon Bank to the Pokémon Home app on your Switch.
Note:
* You will need a Nintendo Network ID to use Pokémon Bank.
* Pokémon Bank requires a paid subscription.
* Pokémon Home is also a paid service.
* Not all Pokémon are transferable through these methods.
Therefore, you can migrate your Pokémon from Diamond to other games without needing an Action Replay, but it requires a bit more work and some paid services.