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The paper introduces covariance-controlled adaptive Langevin thermostat (CCAdL), a Bayesian sampling method based on stochastic gradients (SG) that aims to account for correlated errors introduced by the SG approximation of the true gradient. The authors demonstrate that CCAdL is more accurate and robust than other SG based methods on various test problems. In general, the paper is well written but sometimes a bit hard to follow for someone who is not familiar with these type of sampling algorithms. The paper starts by reviewing various SG methods for efficient Bayesian posterior sampling (SGDL, mSGDL, SGHMC, SGHNT). It would be quite helpful if the authors could provide, for example, a table or figure that gives on overview over the different SG variants and highlights their commonalities and differences.