Invasive plants are an increasing threat to global biodiversity. Effective management depends on accurate predictions of their spread. However, modelling the geographic distribution of invasive species, particularly with correlative species distribution models (SDMs), is challenging. SDMs assume that species are in equilibrium with their environment (i.e., they occur in all suitable environments); this assumption is likely to be violated for a species that is actively invading new environments. This assumption is rarely assessed, and when violated can have consequences for model reliability. Using the invasive vine Vincetoxicum rossicum, we tested the hypotheses that: 1) invasive species’ distribution in environmental and geographic space increase to a plateau over time; 2) this plateau is a useful proxy for equilibrium distribution, a key assumption underlying SDMs. We compare V. rossicum’s expansion in environmental and geographic space between historical and current time periods and infer equilibrium when its distribution has remained stable for an extended period. We also compare the performance of SDMs from historical time periods in predicting the current geographic distribution of V. rossicum. We found that V. rossicum has reached equilibrium in environmental space, but is still expanding its geographic distribution. SDM performance was poor in the first 30 years following introduction, but improved as V. rossicum approached environmental equilibrium. Our findings demonstrate the power of including temporal dynamics and the need to consider environmental and geographic equilibrium separately when modelling the distribution of invasive species. In light of our findings, we address shortcomings of the current approach to defining an equilibrium distribution and present a new perspective for reconciling the potentially confounding influence of dispersal limitation when assessing equilibrium distribution.