The following quote from St. Augustine should be of interest to LDS readers.
But God forbid that we should meet him with such an assertion as he says certain persons advance against him: “That man is placed on an equality with God, if he is described as being without sin;” as if indeed an angel, because he is without sin, is put in such an equality. For my own part, I am of this opinion that the creature will never become equal with God, even when so perfect a holiness shall be accomplished in us, that it shall be quite incapable of receiving any addition. No; all who maintain that our progress is to be so complete that we shall be changed into the substance of God, and that we shall thus become what He is, should look well to it how they build up their opinion; for myself I must confess that I am not persuaded of this. (On Nature and Grace, chapter 37)
I believe this indicates that some Christians even as late as St. Augustine believed that those who are saved will “become what [God] is” and that their “substance” will “be changed into the substance of God.” The word “substance” should be interesting to anyone who has studied early Christianity. The early Christians used “substance” as a code word for “same nature.” The Father, Son, and Holy Ghost are said to be of one substance, that is, each is of the same nature.
Food for thought.