An aubade is a poem that either welcomes or laments the morning. In his poem “The Good-Morrow,” John Donne hints at the aubade tradition but changes it significantly to suit his purpose.
The poem begins with a reflection on what the speaker and his beloved did before they fell in love. The speaker wonders if they were simply asleep or caught up in mere fleeting pleasures. He asks himself, too, if the beauty he saw and recognized then was “but a dream” of his beloved.
Now it is morning for the lovers' souls. Here's where the nod toward the aubade comes in. It is not literally morning in the poem, or at least not explicitly literally morning, but the souls of the lovers are awakening to the joys of their love. The night is over, and they are greeting a new “day” together, a “day” in which their love takes control of them and they explore the world together while exploring each other. Their love has expanded them. It has brightened them. The sun of love has risen in their hearts.
Notice that the speaker is not praising or welcoming the morning in itself as a true aubade does. Rather he is turning the morning into a symbol of the lovers' new existence together. This is what he is welcoming and praising as he reflects on his unity with his beloved.