In a large stock pot combine the lime juice, coconut milk, wine, curry paste, garlic, fish sauce and sugar. Stir to dissolve sugar and curry paste and bring to a boil over high heat. Boil for 2 minutes then add mussels. Cover and cook, stirring occasionally until mussels are opened, 5 to 8 minutes. Some mussels may take a bit longer to open.
Remove from the heat. Pour mussels and liquid into a serving dish and toss with coriander.