There is only one form of infinite love. It is a love with no conditions.
There is no part of another person, or oneself, that is static. All can change given time. If a component of a person is loved, that love is exposed to the currents of time. Therefore, that love cannot be infinite, as the waves will grind it into sand.
But time will never erode unconditional love. If love has no conditions, such as common interests, physical appearance, and qualities of personality, then any change will have no affect upon it.
Conditional love is an effect of someone meeting our finite requirements, unconditional love is an infinite cause of love no matter what the other's thoughts or actions.
Love without conditions is the perfect expression of our infinity. With it we take the most powerful emotion and use it to give ourselves to someone knowing that there is no right or wrong way to live, only infinite possibilities.
So what is the unconditional that this love targets? It's hard to say, other than what is simply an attempt to put into words that which lies beyond language. Perhaps two people can find it expressed in a poem or a song, but that expression will only ever expose the peak of the mountain, not all the complexity of the peaks and crevasses that ascend up to it.