The proportionality between global mean temperatures and cumulative emissions is the foundation of carbon budgeting frameworks, and deviations from this behavior could impact estimates of required net zero timings and negative emissions requirements to meet the requirements of the Paris Agreement. However, existing Earth System Model diagnostic experiments do not contain direct measurements of these deviations.  Here we propose an efficient set of ESM diagnostic experiments for the assessment of transient climate response to cumulative emissions (TCRE), zero emissions commitment (ZEC),  and a set of climate reversibility metrics in an emissions-driven framework, together with an initial application in a subset of existing complex and simple climate models.  The base experiment flat10 is a constant emissions flux of CO₂ and provides near-consistent estimates of TCRE with existing concentration-based approaches, and that the ZEC defined in a branch experiment flat10-zec is generally slightly reduced compared with estimates branching from the CMIP6 1pctCO2 experiment, where compatible emissions are strongly weighted towards the end of the emissions period.   A final experiment flat10-cdr assesses climate reversibility under negative emissions, with indications that several of the ESMs considered have ocean dynamical responses which cause asymmetries in the response to positive and negative emissions beyond that which would be expected from ZEC alone.  We propose that these experiments have applications in future CMIP exercises both for the estimation of emissions driven diagnostics and  the calibration of climate emulators.