I think from Union station by Metrolink...
from 7 and metro train you go catch the train that takes you to Union station and then at Union station you take the Metrolink as said above.
Take the Red or purple lines downstairs to Union Station or you can take the Redline into North Hollywood then transfer to the Orange line, which is a bus, and that should get you there.
Take any train to union station, then you can
7th St/Metro Center connects with Union Station via the Red or Purple lines. From there the daily Amtrak train to San Diego stops at the Carlsbad station.
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