Diabatic processes are important contributors to cyclone intensification. However, precisely quantifying this contribution, and how it may change in a warming world, has remained a challenge. Previous frameworks use simplifying assumptions that constrain their applicability and limit their use to certain parts of the cyclone lifecycle. In this study, we develop a cyclone-centric Potential Vorticity (PV) framework to quantify the contribution from various processes to cyclonic PV intensification and to the maximum relative vorticity that cyclones attain. Applying this framework to cyclones tracked on model runs, we find that the PV intensification in the low-level cyclone is almost entirely associated with the in-situ PV generation from diabatic sources, both for summer and winter. The diabatic contribution to the maximum relative vorticity increases with cyclone strength, from about 35 % for a median cyclone to 85 % for the strongest cyclones in winter. With warming, low-level winter cyclones show a stronger increase in strength with warming than summer cyclones, which for the strongest cyclones can be attributed to winter cyclones being able to more easily utilise the increase in moisture due to their stronger vertical winds. For the strongest cyclones in both seasons, the vertical wind response with warming decreases the downward penetration of upper-level PV during cyclone intensification, consistent with the low-level cyclones being more diabatically driven. These results point to a "strong gets stronger" response of cyclones with warming, especially in winter, with important implications for extreme weather impacts of global warming.