Abstract Particulate organic carbon (POC) fluxes are important for the marine carbon cycle; however, these fluxes are highly variable in both space and time. Consequently, current estimates retain high uncertainty when predicting POC flux from environmental drivers because the influence of pulse events is not adequately accounted for. Here, by using a hierarchical Bayesian regression model, we explicitly and simultaneously model the mean and variance of POC flux as a function of environmental variables. Our model reproduces the observed distribution of POC fluxes by accounting for flux variance, and estimates global POC flux at ∼6 GtC yr−1 ${text{yr} }^{-1}$ at 100 m, of which 52% $%$ is due to the influence of episodic pulse events. Additionally, spatial patterns in vertical attenuation rates and its stochasticity can be estimated. Therefore, quantifying the small‐scale variability introduced through pulse events may be equally as important as understanding specific export pathways.