  This paper presents a novel approach to audio restoration, focusing on the
enhancement of low-quality music recordings, and in particular historical ones.
Building upon a previous algorithm called BABE, or Blind Audio Bandwidth
Extension, we introduce BABE-2, which presents a series of significant
improvements. This research broadens the concept of bandwidth extension to
\emph{generative equalization}, a novel task that, to the best of our
knowledge, has not been explicitly addressed in previous studies. BABE-2 is
built around an optimization algorithm utilizing priors from diffusion models,
which are trained or fine-tuned using a curated set of high-quality music
tracks. The algorithm simultaneously performs two critical tasks: estimation of
the filter degradation magnitude response and hallucination of the restored
audio. The proposed method is objectively evaluated on historical piano
recordings, showing a marked enhancement over the prior version. The method
yields similarly impressive results in rejuvenating the works of renowned
vocalists Enrico Caruso and Nellie Melba. This research represents an
advancement in the practical restoration of historical music.
