Permanently anoxic regions in the ocean are widespread and exhibit unique microbial metabolic activity exerting substantial influence on global elemental cycles and climate. Reconstructing microbial metabolic activity rates in these regions has been challenging, due to the technical difficulty of direct rate measurements. In Cariaco Basin, which is the largest permanently anoxic marine basin and an important model system for geobiology, long‐term monitoring has yielded time series for the concentrations of biologically important compounds; however, the underlying metabolite fluxes remain poorly quantified. Here, we present a computational approach for reconstructing vertical fluxes and in situ net production/consumption rates from chemical concentration data, based on a 1‐dimensional time‐dependent diffusive transport model that includes adaptive penalization of overfitting. We use this approach to estimate spatiotemporally resolved fluxes of oxygen, nitrate, hydrogen sulfide, ammonium, methane, and phosphate within the sub‐euphotic Cariaco Basin water column (depths 150–900 m, years 2001–2014) and to identify hotspots of microbial chemolithotrophic activity. Predictions of the fitted models are in excellent agreement with the data and substantially expand our knowledge of the geobiology in Cariaco Basin. In particular, we find that the diffusivity, and consequently fluxes of major reductants such as hydrogen sulfide, and methane, is about two orders of magnitude greater than previously estimated, thus resolving a long‐standing apparent conundrum between electron donor fluxes and measured dark carbon assimilation rates.