In active learning, new labels are commonly acquired in batches. However, common acquisition functions are only meant for one-sample acquisition rounds, and when their scores are used naively for batch acquisition, they result in batches lacking diversity, which negatively impacts performance. State-of-the-art batch acquisition functions are very costly to compute on the other hand. In this paper, we present a novel class of stochastic acquisition functions that extend one-sample acquisition functions to the batch setting by observing that the computed acquisition scores are only really valid for the first sample that is selected in every batch acquisition round and that there is an increasing error in the scores for future samples in the batch. We model this error in the scores for additional batch samples. We acquire new samples by sampling from the pool set using the adapted scores. Our acquisition functions are both vastly cheaper to compute and out-perform other batch acquisition functions.