The pattern of neural activity evoked by a stimulus can be substantially affected by ongoing spontaneous activity. Separating these two types of activity is particularly important for calcium imaging data given the slow temporal dynamics of calcium indicators. Here we present a statistical model that decouples stimulus-driven activity from low dimensional spontaneous activity in this case. The model identifies hidden factors giving rise to spontaneous activity while jointly estimating stimulus tuning properties that account for the confounding effects that these factors introduce. By applying our model to data from zebrafish optic tectum and mouse visual cortex, we obtain quantitative measurements of the extent that neurons in each case are driven by evoked activity, spontaneous activity, and their interaction. By not averaging away potentially important information encoded in spontaneous activity, this broadly applicable model brings new insight into population-level neural activity within single trials.