How can I remedy my infant's nighttime separation anxiety?

It's You. It's really, probably your own anxiety, not your infant. How do you know your infant is anxious? Those are your feelings. Behavioral insomnia in infants is quite common and is perpetuated by attending to the infant each and every time they wake up at night. You should not sleep with your infant, he or she needs to be in another room. After 6 months, a full nights sleep will occur if you ignore.
Extinguish slowly. At night, a thorough routine that is always followed is key. That way they know what is coming, and there is bed at the end. If there is a lot of anxiety at first and they scream until you come in and "hang out", then do that. Start sitting close, pay minimal attention, then every few nights, start sitting closer to the door. They slowly get used to you being further away, then out of the room.