International Ocean Discovery Program (IODP) Site U1437 recovered an 1,800‐m‐long sediment sequence in a volcano‐bounded basin on the Izu rear arc. Pore fluid studies revealed a pattern of repeated fluid inputs, fluid diffusion, and methane and ethane accumulations, which represent “fluid anomalies” that disturb the fluid profiles. First‐order reversal curve analysis, magnetic hysteresis, saturation isothermal remanent magnetization, and low‐temperature remanence cycling reveal a detrital input dominated by vortex‐state and multidomain magnetite, which passes through an initial stage of partial magnetite dissolution and greigite authigenesis in the upper few tens of meters. Progressive magnetic mineral diagenesis comprises the continued loss of fine‐grained magnetite and gradual pyritization of greigite and produces a background logarithmic decrease in saturation isothermal remanent magnetization normalized by magnetic susceptibility. This process implies a continuing slow supply of S²⁻ to depths >1,500 m. Thermally driven diagenesis, which would cause extensive loss of greigite at these depths, does not appear to be significant here. Multidomain magnetite grains dominate the magnetic mineralogy in the deepest part of the sequence, but some single‐domain magnetite survives as inclusions in silicates. Fluid anomalies representing sulfate influx drive locally renewed greigite authigenesis, as do methane and ethane accumulations. In some cases, where methane is accompanied by H₂S (“sour gas”), fine‐grained greigite is converted to pyrite. We term these multiple episodes of enhanced magnetic mineral alteration “punctuated magnetic mineral diagenesis.” Despite both progressive and punctuated magnetic mineral diagenesis, enough depositional remanence survives to allow recognition of the magnetostratigraphy to 1,320 m below seafloor.