It’s referred to as divinization in the west. It’s not as emphasized as in the east, but it’s a part of both traditions.
To quote the Catechism of the Catholic Church:
460 The Word became flesh to make us “partakers of the divine nature”:78 "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God."79 "For the Son of God became man so that we might become God."80 "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods."81
602 Consequently, St. Peter can formulate the apostolic faith in the divine plan of salvation in this way: "You were ransomed from the futile ways inherited from your fathers… with the precious blood of Christ, like that of a lamb without blemish or spot. He was destined before the foundation of the world but was made manifest at the end of the times for your sake."402 Man’s sins, following on original sin, are punishable by death.403 By sending his own Son in the form of a slave, in the form of a fallen humanity, on account of sin, God “made him to be sin who knew no sin, so that in him we might become the righteousness of God.”
1988 Through the power of the Holy Spirit we take part in Christ’s Passion by dying to sin, and in his Resurrection by being born to a new life; we are members of his Body which is the Church, branches grafted onto the vine which is himself:36
[INDENT][God] gave himself to us through his Spirit. By the participation of the Spirit, we become communicants in the divine nature. . . . For this reason, those in whom the Spirit dwells are divinized.37
2009 Filial adoption, in making us partakers by grace in the divine nature, can bestow true merit on us as a result of God’s gratuitous justice. This is our right by grace, the full right of love, making us “co-heirs” with Christ and worthy of obtaining "the promised inheritance of eternal life."60 The merits of our good works are gifts of the divine goodness.61 "Grace has gone before us; now we are given what is due. . . . Our merits are God’s gifts."62[/INDENT]