  With the development of audio playback devices and fast data transmission,
the demand for high sound quality is rising for both entertainment and
communications. In this quest for better sound quality, challenges emerge from
distortions and interferences originating at the recording side or caused by an
imperfect transmission pipeline. To address this problem, audio restoration
methods aim to recover clean sound signals from the corrupted input data. We
present here audio restoration algorithms based on diffusion models, with a
focus on speech enhancement and music restoration tasks. Traditional
approaches, often grounded in handcrafted rules and statistical heuristics,
have shaped our understanding of audio signals. In the past decades, there has
been a notable shift towards data-driven methods that exploit the modeling
capabilities of DNNs. Deep generative models, and among them diffusion models,
have emerged as powerful techniques for learning complex data distributions.
However, relying solely on DNN-based learning approaches carries the risk of
reducing interpretability, particularly when employing end-to-end models.
Nonetheless, data-driven approaches allow more flexibility in comparison to
statistical model-based frameworks, whose performance depends on distributional
and statistical assumptions that can be difficult to guarantee. Here, we aim to
show that diffusion models can combine the best of both worlds and offer the
opportunity to design audio restoration algorithms with a good degree of
interpretability and a remarkable performance in terms of sound quality. We
explain the diffusion formalism and its application to the conditional
generation of clean audio signals. We believe that diffusion models open an
exciting field of research with the potential to spawn new audio restoration
algorithms that are natural-sounding and remain robust in difficult acoustic
situations.
