2 Peter 1:4 (NAS): For by these He has granted to us His precious and magnificent promises, so that by them you may become partakers of the divine nature, having escaped the corruption that is in the world by lust.
The word partaker means sharer, associate, partner.
Divine comes from the Greek word translated God.
Nature is genus or sort as in “Jews by nature/ birth” (Galatians 2:15).
One other passage that uses this expression “divine nature” is Acts 17:
Acts 17:29 (NAS): Being then the children of God, we ought not to think that the Divine Nature is like gold or silver or stone, an image formed by the art and thought of man.
In other words the divine nature is not made with hands, nor is it of the flesh. It is heavenly or spiritual.
The promises of the Hebrew Scriptures concerning the Messiah and His kingdom were all about allowing his people to become partakers of the divine nature. In other words, His desire was to disclose the way that humanity could enter back into the garden (His presence).
Now, these saints had partaken of the divine nature in that they escaped corruption that is in the world below because of lust. This word escape is only used by Peter, and he later indicates that it is done through “the knowledge of our Lord and Savior Jesus Christ” (2 Peter 2:20).
Another way to say this is that they born again not of perishable seed but imperishable: the word of God, the gospel (1 Peter 1:23).
The word corruption in our original passage is used a handful of times in the New Testament:
Romans 8:21 (NAS): that the creation itself also will be set free from its slavery to corruption into the freedom of the glory of the children of God.
1 Corinthians 15:42 (NAS): So also is the resurrection of the dead. It is sown a perishable body, it is raised an imperishable body;
1 Corinthians 15:50 (NAS): Now I say this, brethren, that flesh and blood cannot inherit the kingdom of God; nor does the perishable inherit the imperishable.
Galatians 6:8 (NAS): For the one who sows to his own flesh will from the flesh reap corruption, but the one who sows to the spirit will from the Spirit reap eternal life.
Colossians 2:20–23 (NAS): If you have died with Christ to the elementary principles of the world, why, as if you were living in the world, do you submit yourself to decrees, such as,
21 “Do not handle, do not taste, do not touch!”
22 (which all refer to things destined to perish with use)—in accordance with the commandments and teachings of men?
23 These are matters which have, to be sure, the appearance of wisdom in self-made religion and self-abasement and severe treatment of the body, but are of no value against fleshly indulgence.
2 Peter 2:12–16 (NAS): But these, like unreasoning animals, born as creatures of instinct to be captured and killed, reviling where they have no knowledge, will in the destruction of those creatures also be destroyed,
13 suffering wrong as the wages of doing wrong. They count it a pleasure to revel in the daytime. They are stains and blemishes, reveling in their deceptions, as they carouse with you,
14 having eyes full of adultery that never cease from sin, enticing unstable souls, having a heart trained in greed, accursed children;
15 forsaking the right way, they have gone astray, having followed the way of Balaam, the son of Beor, who loved the wages of unrighteousness;
16 but he received a rebuke for his own transgression, for a mute donkey, speaking with a voice of a man, restrained the madness of the prophet.
2 Peter 2:17–19 (NAS): These are springs without water and mists driven by a storm, for whom the black darkness has been reserved.
18 For speaking out arrogant words of vanity they entice by fleshly desires, by sensuality, those who barely escape from the ones who live in error,
19 promising them freedom while they themselves are slaves of corruption; for by what a man is overcome, by this he is enslaved.
All of these passages relate on way or another to eschatology.
The passage in Galatians follows a lengthy allegory about the children of the flesh versus the children of the spirit (Galatians 4). The end of that text is a passage of judgement: the children of the bond woman who persecuted the children of promise would be cast out.
In Colossians, Paul had been discussing how the feast days were shadows of good things about to come, and he was about to talk about the need for the church to emphasize things above so that they could participate in the transformation from the old man to the new man so that God may be all in all (cf. 1 Corinthians 15:58).
The texts in Peter are in a discussion of the judgement that was about to come on those who were trying to mislead and harm those that followed Christ (2 Peter 2:1ff). In chapter 3, he would discuss how those elements of the law (see the Colossians text above) would be done away with.
As we look at the Romans passage, we quickly see that it too is in the midst of a lengthy discussion of Law versus grace and flesh versus spirit (Romans 5-8). He says, however, in Romans 8:18 that the glory was about to be revealed (NRSV).
1 Corinthians 15 is about the same transformation of Romans 8 and Colossians 3, from the old man of the flesh to the new man of the spirit. He even says in verse 56, “The sting of death is sin, and the power of sin is the Law.”
This is further seen by his reference to flesh and blood not being able to enter the kingdom. This is a reference to Jesus' teaching of the need for being born of above that can be found in John 3:1ff. It's the same new birth of 1 Peter 1: a transition from hyper-dependence on the flesh (silver and gold) to trusting in the heavenly (blood of Christ).
Peter's comment about being transformed from the corruption of the world to the divine nature is no different than Paul's discussion of resurrection in Romans 8 and 1 Corinthians 15. It is also the same as his comments on the transition between Law and grace as found in Galatians and Colossians.
As a final note, Peter says in 2 Peter 1:11, “…for in this way the entrance into the eternal kingdom of our Lord and Savior Jesus Christ will be abundantly supplied to you.” Again, that's exactly Paul's message in 1 Corinthians 15:50.
Resurrection isn't a transformation of our physical bodies but a reorientation of our lives from the flesh to the spirit.