Projections of future emissions based on current trends are vital to assess the performance of mitigation efforts and to devise mitigation strategies. Several studies have investigated the aspiration gap between projected emissions and global warming targets, but it is as yet uncertain how changes in consumption patterns may impact trajectories. Here we employ a Markov Chain Monte Carlo (MCMC) Bayesian analysis of historical and projected consumption-based emissions during 1995-2050 via a modified Kaya identity. We assume regional convergence over time after finding strong supporting historical evidence. We find global emissions of 27-62 GtCO2eq yr-1 by 2050, slightly higher than SSP1-2.6 and encompassing SSP4-6.0, resulting in 1.9-2.4°C of warming above pre-industrial levels mid-way through the century. The median projection shows a 2024 peak of 55 GtCO2eq yr-1 and an annual average decrease of 0.58 GtCO2eq thereafter. Future emission decreases result from the interplay between a rapid reduction driven by decreasing emission intensities, especially in housing, and the change of final demand structure (-53 GtCO2eq yr-1) against increases from economic and population growth (+44 GtCO2eq yr-1). Compared to other work, we find an earlier peak which is lower in magnitude. This is due to the inclusion of recent data, the consideration of regional convergence, and the incorporation of structural changes in final demand as explanatory variables. This highlights the importance in continually updating projections and considering models that reflect convergence and demand structure changes, in order to better inform climate policy.