For the best performance, Alyssum seeds should be sown in early spring when temperatures are warming. Alyssum seedlings cannot withstand a heavy frost. In warmer climates, Sweet Alyssum flower seeds will self-sow year after year. Alyssum care includes keeping the plants well watered throughout the summer and lightly trimming the Sweet Alyssum plant back after blooming to neaten the appearance and encourage another flush of flowers.