  Score-based generative models (SGMs) have recently shown impressive results
for difficult generative tasks such as the unconditional and conditional
generation of natural images and audio signals. In this work, we extend these
models to the complex short-time Fourier transform (STFT) domain, proposing a
novel training task for speech enhancement using a complex-valued deep neural
network. We derive this training task within the formalism of stochastic
differential equations (SDEs), thereby enabling the use of predictor-corrector
samplers. We provide alternative formulations inspired by previous publications
on using generative diffusion models for speech enhancement, avoiding the need
for any prior assumptions on the noise distribution and making the training
task purely generative which, as we show, results in improved enhancement
performance.
