This paper investigates the concurrent effects on regional disparities of the speeds of innovation and of the spatial diffusion of knowledge. The aim is to investigate whether an increase in the pace of innovation, identical in all regions, due to exogenous factors such as the «technological revolution» or policies targeting the «innovative effort» of territories, can give rise to increased disparities. In order to answer these questions, the paper focuses on the role of interregionally shared knowledge and shows that, due to the cumulativeness of knowledge, making the same innovative effort is not enough to maintain the same income per capita. Moreover, the speed of innovation is not the only determinant, because a role of equal importance is played by the ease of interregional knowledge diffusion. To support this argument, first a new simple static model is built to extend symmetrically existing north-south models of trade and to rigorously represent the actual producers of goods whose production technique is shared between regions. Then, building on the first model, two reduced forms for the dynamics of innovation and diffusion flows are introduced - one probabilistically, the other with multiple equilibria. These lead to the same conclusion: an increase in the pace of innovation, even with structurally identical regions, may generate regional income disparities if knowledge is cumulative and spillovers are essentially local. It is finally shown, however, that the divergence effect of increased innovation pace can be counterbalanced by an increase in the speed of spatial knowledge diffusion.