We present a microscopic theory of the amplified spontaneous emission of a spectrally broadband quantum dot superluminescent diode within the quantum white noise limit. From this multimode quantum theory, we have the ability to obtain all orders of temporal correlation functions. In particular, we derive rate equations for the optical power densities, the level occupation of inhomogeneous ensemble of quantum dots within the diode, as well as the emitted optical spectra. As the main result, we find the external power spectrum as a convolution of the intra-diode photon spectrum with a Lorentzian response. Assuming a Gaussian light-matter coupling results in a similar shaped Gaussian output spectrum, which agrees very well with available experimental data.Keywords: quantum dot superluminescent diodes, power spectrum, ASE, amplified spontaneous emission, photon statistics, quantum dot, quantum fluctuation, Ito formalism, input-output formalism, quantum stochastic differential equations, multimode laser theory, rate equations, correlation function.