Extreme weather events are expected to increase in frequency and intensity in response to higher global temperatures, augmenting societal exposure to these events. While the magnitude of projected changes in extremes varies considerably among future emission scenarios, a large part of this uncertainty is driven by the choice of scenario, rather than by the climate response to a particular emission scenario. A growing body of research has identified robust linear relationships between climate changes and cumulative carbon emissions; for global average temperature change, this relationship is known as the transient climate response to cumulative carbon emissions (TCRE). Extensions of the TCRE framework to other variables, such as regional and seasonal temperature and precipitation changes, have also shown to be effective, raising the possibility that changes in weather extremes could be linked to cumulative carbon dioxide (CO2) emissions. Here, we estimate changes in historical and projected trends in one-day (Rx1day) and five-day maximum precipitation (Rx5day) events as a function of cumulative carbon emissions across a range of future emission scenarios and global climate models. Our results show that median Rx1day and Rx5day generally increases linearly with increasing cumulative emissions, consistent with studies that have previously employed the TCRE framework to estimate changes in precipitation extremes, as well as other climate indicators. Overall, we show that a linear response to cumulative CO2 emissions is a good approximation for both historical and future trends in precipitation extremes.