Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally but cannot correct errors in modelled spatial patterns. Here we propose a framework based on physically constrained generative adversarial networks to improve local distributions and spatial structure simultaneously. We apply our approach to the computationally efficient CM2Mc–LPJmL ESM. Our method outperforms existing ones in correcting local distributions and leads to strongly improved spatial patterns, especially regarding the intermittency of daily precipitation. Notably, a double-peaked Intertropical Convergence Zone, a common problem in ESMs, is removed. Enforcing a physical constraint to preserve global precipitation sums, the generative adversarial network can generalize to future climate scenarios unseen during training. Feature attribution shows that the generative adversarial network identifies regions where the ESM exhibits strong biases. Our method constitutes a general framework for correcting ESM variables and enables realistic simulations at a fraction of the computational cost.Earth system models (ESMs) are powerful tools for simulating climate fields, but weather forecasting and in particular precipitation prediction with ESMs are challenging. A generative adversarial network, constrained by the sum of global precipitation, is developed that substantially improves ESM predictions of spatial patterns and intermittency of daily precipitation.