We present a new model for oxic and anoxic diagenesis of shallow and deep-sea sediments based on an efficient solver for steady state pore water and solid phase diffusion/reaction/advection equations. The model, called Muds, is orders of magnitude faster than solvers of the corresponding time-dependent equations. The model resolves Mn and Fe/S geochemistry as well as pore water pH and CaCO3 dissolution. The model speed opens application possibilities that are impossible for time-dependent models, including automatic tuning of uncertain parameters, and deployment of the model in gridded global domains. The kinetic rate constants for respiration and bioturbation are parameterized as functions of the organic carbon rain to the seafloor, based on existing parameterizations in the literature. Seven uncertain model parameters, including many of the rate constant parameterizations, were tuned to minimize the misfit to observations from 53 sedimentary locations throughout the ocean. The model tuning knobs were the fractions of labile and refractory organic matter in the sedimenting material, the NO3-, Mn, Fe, and S respiration rate constant parameterizations, and the depth scales of respiration and of pore water irrigation. We searched for adequate fit values of these parameterizations using a simulated annealing method. The cost function (degree of misfit) was based on a comparison of pore water (NO3-, NH4+, Mn2+, and Fe2+) and solid phase (organic carbon and MnO2) model results with data. Many of the tuning parameters are constrained to ¿50% or better. The model is most skillful at predicting organic carbon concentration, depth of NO3- penetration, and pore water Fe2+, and less so for Mn2+, NH4+, and solid phase MnO2. The model misses some of the very high sediment surface MnO2 concentrations observed in, for example, the California Borderlands. We believe that these sites must receive a higher input of reactive Mn than the crustal abundance of the clay rain. The model was deployed on every 2¿ ¿ 2¿ grid point below 1000 m of the global seafloor, using gridded maps of organic carbon rain to the seafloor and overlying water chemistry. The deep-sea carbon burial efficiency is 7%, with 95% of respiration by oxic metabolism. The model was also run against a new depth-oxygen hypsometry of the global ocean, with sediment area as a function of overlying oxygen concentration and average depth related to carbon fluxes, to include the effects of shallow water sediments. This analysis predicts that shallow waters (<1000 m) account for 88% of respiration, and oxygen accounts for 66% of respiration overall. Denitrification is closely coupled to organic nitrogen fluxes to the sediment, and the global rate is estimated to be 1.4 ¿ 1014 mol yr-1, a factor of 6--8 higher than the corresponding estimate from Middelburg et al. <1996>, throwing the nitrogen cycle in the ocean into imbalance.