Aim: To propose a species distribution modelling framework and its companion "iSDM" R package for predicting the potential and realized distributions of invasive species within the invaded range. Location: Northern France. Methods: The non-equilibrium distribution of invasive species with the environment within the invaded range affects the environmental representativeness of species presence-absence data collected from the field and introduces uncertainty in observed absences as these may either reflect unsuitable sites or be incidental. To address these issues, we here propose an environmental systematic sampling design to collect presence-absence data from the field and a probability index to sort and subsequently separate environmental absences (EAs: reflecting environmentally unsuitable sites) from dispersal-limited absences (DLAs: reflecting sites out of dispersal reach). We first conducted a comprehensive test based on a virtual species to evaluate the performance of our framework. Then, we applied it on different life stages of a non-native tree species (Prunus serotina Ehrh.) invasive in Europe. Results: Regarding the potential distribution, we found higher model performances for both the virtual species (true skill statistics (TSS) > 0.75) and P. serotina (TSS >= 0.68) after carefully selecting absences with a low probability to be DLAs compared with classical models that incorporate both EAs and DLAs (e.g. TSS = 0.11 for P. serotina with 80% of DLAs). On the contrary, both EAs and DLAs as well as dispersal-related covariates were needed to capture the realized distribution of both the virtual species and P. serotina. Main Conclusions: Our framework helps overcoming the conceptual and methodological limitations of the disequilibrium in species' distribution models inherent to invasive species and enables managers to robustly estimate both the realized and potential distributions of invasive species. Although more relevant for modelling the distribution of non-native species, this framework can also be applied to native species.