  This paper introduces UnDiff, a diffusion probabilistic model capable of
solving various speech inverse tasks. Being once trained for speech waveform
generation in an unconditional manner, it can be adapted to different tasks
including degradation inversion, neural vocoding, and source separation. In
this paper, we, first, tackle the challenging problem of unconditional waveform
generation by comparing different neural architectures and preconditioning
domains. After that, we demonstrate how the trained unconditional diffusion
could be adapted to different tasks of speech processing by the means of recent
developments in post-training conditioning of diffusion models. Finally, we
demonstrate the performance of the proposed technique on the tasks of bandwidth
extension, declipping, vocoding, and speech source separation and compare it to
the baselines. The codes are publicly available.
