Understanding how individual pollution sources contribute to ambient sulfate pollution is critical for assessing past and future air quality regulations. Since attribution to specific sources is typically not encoded in spatial air pollution data, we develop a mechanistic model which we use to estimate, with uncertainty, the contribution of ambient sulfate concentrations attributable specifically to sulfur dioxide (SO2) emissions from individual coal-fired power plants in the central United States. We propose a multivariate Ornstein–Uhlenbeck (OU) process approximation to the dynamics of the underlying space-time chemical transport process, and its distributional properties are leveraged to specify novel probability models for spatial data that are viewed as either a snapshot or time-averaged observation of the OU process. Using US EPA SO2 emissions data from 193 power plants and state-of-the-art estimates of ground-level annual mean sulfate concentrations, we estimate that in 2011—a time of active power plant regulatory action—existing flue-gas desulfurization (FGD) technologies at 66 power plants reduced population-weighted exposure to ambient sulfate by 1.97 μg/m3 (95% CI: 1.80–2.15). Furthermore, we anticipate future regulatory benefits by estimating that installing FGD technologies at the five largest SO2-emitting facilities would reduce human exposure to ambient sulfate by an additional 0.45 μg/m3 (95% CI: 0.33–0.54). Supplementary materials for this article are available online.