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Under the UN-Decade of Ecosystem Restoration and Bonn Challenge, second-growth forest is promoted as a global solution to climate change, degradation and associated losses of biodiversity and ecosystem services. Second growth is often invaded by alien tree species and understanding how this impacts carbon stock and biodiversity recovery is key for restoration planning. We assessed carbon stock and tree diversity recovery in second growth invaded by two Acacia species and non-invaded second growth, with associated edge effects, in the Brazilian Atlantic Forest. Carbon stock recovery in non-invaded forests was threefold lower than in invaded forests. Increasingly isolated, fragmented and deforested areas had low carbon stocks when non-invaded, whereas the opposite was true when invaded. Non-invaded forests recovered threefold to sixfold higher taxonomic, phylogenetic and functional diversity than invaded forest. Higher species turnover and lower nestedness in non-invaded than invaded forests underpinned higher abundance of threatened and endemic species in non-invaded forest. Non-invaded forests presented positive relationships between carbon and biodiversity, whereas in the invaded forests we did not detect any relationship, indicating that more carbon does not equal more biodiversity in landscapes with high vulnerability to invasive acacias. To deliver on combined climate change and biodiversity goals, restoration planning and management must consider biological invasion risk. This article is part of the theme issue 'Understanding forest landscape restoration: reinforcing scientific foundations for the UN Decade on Ecosystem Restoration'.