Tropical peat swamp forests (PSFs) are globally important carbon stores under threat. In Southeast Asia, 35% of peatlands had been drained and converted to plantations by 2010, and much of the remaining forest had been logged, contributing significantly to global carbon emissions. Yet, tropical forests have the capacity to regain biomass quickly and forests on drained peatlands may grow faster in response to soil aeration, so the net effect of humans on forest biomass remains poorly understood. In this study, two lidar surveys (made in 2011 and 2014) are compared to map forest biomass dynamics across 96 km2 of PSF in Kalimantan, Indonesia. The peatland is now legally protected for conservation, but large expanses were logged under concessions until 1998 and illegal logging continues in accessible portions. It was hypothesized that historically logged areas would be recovering biomass while recently logged areas would be losing biomass. We found that historically logged forests were recovering biomass near old canals and railways used by the concessions. Lidar detected substantial illegal logging activity—579 km of logging canals were located beneath the canopy. Some patches close to these canals have been logged in the 2011–2104 period (i.e. substantial biomass loss) but, on aggregate, these illegally logged regions were also recovering. Unexpectedly, rapid growth was also observed in intact forest that had not been logged and was over a kilometre from the nearest known canal, perhaps in response to greater aeration of surface peat. Comparing these results with flux measurements taken at other nearby sites, we find that carbon sequestration in above‐ground biomass may have offset roughly half the carbon efflux from peat oxidation. This study demonstrates the power of repeat lidar survey to map fine‐scale forest dynamics in remote areas, revealing previously unrecognized impacts of anthropogenic global change.