Tropical forests are diminishing in extent due primarily to the rapid expansion of agriculture, but the future magnitude and geographical distribution of future tropical deforestation is uncertain. Here, we introduce a dynamic and spatially-explicit model of deforestation that predicts the potential magnitude and spatial pattern of Amazon deforestation. Our model differs from previous models in three ways: (1) it is probabilistic and quantifies uncertainty around predictions and parameters; (2) the overall deforestation rate emerges “bottom up”, as the sum of local-scale deforestation driven by local processes; and (3) deforestation is contagious, such that local deforestation rate increases through time if adjacent locations are deforested. For the scenarios evaluated–pre- and post-PPCDAM (“Plano de Ação para Proteção e Controle do Desmatamento na Amazônia”)–the parameter estimates confirmed that forests near roads and already deforested areas are significantly more likely to be deforested in the near future and less likely in protected areas. Validation tests showed that our model correctly predicted the magnitude and spatial pattern of deforestation that accumulates over time, but that there is very high uncertainty surrounding the exact sequence in which pixels are deforested. The model predicts that under pre-PPCDAM (assuming no change in parameter values due to, for example, changes in government policy), annual deforestation rates would halve between 2050 compared to 2002, although this partly reflects reliance on a static map of the road network. Consistent with other models, under the pre-PPCDAM scenario, states in the south and east of the Brazilian Amazon have a high predicted probability of losing nearly all forest outside of protected areas by 2050. This pattern is less strong in the post-PPCDAM scenario. Contagious spread along roads and through areas lacking formal protection could allow deforestation to reach the core, which is currently experiencing low deforestation rates due to its isolation.