While climate science debates are focused on the attainment of peak anthropogenic CO2 emissions and policy tools to reduce peak temperatures, the human‐energy‐climate system can hold “rebound” surprises beyond this peak. Following the second industrial revolution, global per capita CO_{2} emissions (c_{c}) experienced a punctuated growth of about 100% every 60 years, mainly attributable to technological development and its global spread. A model of the human‐energy‐climate system capable of reproducing past punctuated dynamics shows that rebounds in global CO_{2} emissions emerge due to delays intrinsic to the diffusion of innovations. Such intrinsic delays in the adoption and spread of low‐carbon emitting technologies, together with projected population growth, upset the warming target set by the Paris Agreement. To avoid rebounds and their negative climate effects, model calculations show that the diffusion of climate‐friendly technologies must occur with lags one‐order of magnitude shorter (i.e., ∼6 years) than the characteristic timescale of past punctuated growth in c_{c}. Radically new strategies to globally implement the technological advances at unprecedented rates are needed if the current emission goals are to be achieved
