A diffusion combustion start time estimating apparatus for a compression self-igniting internal combustion engine that estimates a diffusion combustion start time when fuel injected at a main injection from a fuel injection valve into a combustion chamber after premixed combustion of an air-fuel mixture has started starts diffusion combustion, wherein the diffusion combustion start time estimating apparatus comprises: a fuel evaporation rate calculating means that calculates an evaporation rate of fuel injected from the fuel injection valve into the combustion chamber by performing a correction on a reference evaporation rate, which is specified in advance, according to at least one of environmental conditions and operating conditions, the evaporation rate being the mass of injected fuel evaporated per unit time; a fuel oxidation rate calculating means that calculates an oxidation rate of fuel forming an air-fuel mixture due to evaporation in the combustion chamber by performing a correction on a reference oxidation rate, which is specified in advance, according to at least one of environmental conditions and operating conditions, the oxidation rate being the mass of fuel that has undergone an oxidation reaction per unit time; and a diffusion combustion start time estimating means that estimates that a diffusion combustion start time of the air-fuel mixture is a time when the fuel evaporation rate calculated by the fuel evaporation rate calculating means and the fuel oxidation rate calculated by the fuel oxidation rate calculating means arrive in a state where the fuel evaporation rate and the fuel oxidation rate match from a state where there is a disparity between the fuel evaporation rate and the fuel oxidation rate, the state where the fuel evaporation rate and the fuel oxidation rate match being a state where the fuel evaporation rate is equal to the fuel oxidation rate. a fuel evaporation rate calculating means that calculates an evaporation rate of fuel injected from the fuel injection valve into the combustion chamber by performing a correction on a reference evaporation rate, which is specified in advance, according to at least one of environmental conditions and operating conditions, the evaporation rate being the mass of injected fuel evaporated per unit time; a fuel oxidation rate calculating means that calculates an oxidation rate of fuel forming an air-fuel mixture due to evaporation in the combustion chamber by performing a correction on a reference oxidation rate, which is specified in advance, according to at least one of environmental conditions and operating conditions, the oxidation rate being the mass of fuel that has undergone an oxidation reaction per unit time; and a diffusion combustion start time estimating means that estimates that a diffusion combustion start time of the air-fuel mixture is a time when the fuel evaporation rate calculated by the fuel evaporation rate calculating means and the fuel oxidation rate calculated by the fuel oxidation rate calculating means arrive in a state where the fuel evaporation rate and the fuel oxidation rate match from a state where there is a disparity between the fuel evaporation rate and the fuel oxidation rate, the state where the fuel evaporation rate and the fuel oxidation rate match being a state where the fuel evaporation rate is equal to the fuel oxidation rate.