The sinking of carbon fixed via net primary production (NPP) into the ocean interior is an important part of marine biogeochemical cycles. NPP measurements follow a log-normal probability distribution, meaning NPP variations can be simply described by two parameters despite NPP's complexity. By analyzing a global database of open ocean particle fluxes, we show that this log-normal probability distribution propagates into the variations of near-seafloor fluxes of particulate organic carbon (POC), calcium carbonate, and opal. Deep-sea particle fluxes at subtropical and temperate time-series sites follow the same log-normal probability distribution, strongly suggesting the log-normal description is robust and applies on multiple scales. This log-normality implies that 29% of the highest measurements are responsible for 71% of the total near-seafloor POC flux. We discuss possible causes for the dampening of variability from NPP to deep-sea POC flux, and present an updated relationship predicting POC flux from mineral flux and depth.