Whisk pomegranate juice, soy sauce, and garlic together in a shallow non-reactive bowl until marinade is well mixed. Add salmon and turn to coat. Cover and marinate for 15 minutes.

Heat olive oil in a skillet over medium heat; add garlic from the marinade and cook until lightly browned, 1 to 2 minutes. Pour in the marinade and cook until reduced and thickened to a glaze, 4 to 5 minutes.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Cook salmon on the preheated grill until flesh flakes easily with a fork, about 3 minutes per side. Serve salmon topped with glaze and garnished with pomegranate seeds.