Machine learning is ready to transform the experimental protocol of birdsong acquisition and playback in ethology and integrative neuroscience. An emerging methodology, known as differentiable digital signal processing (DDSP), allows to train neural networks for machine listening so as to fit the synthesis parameters which correspond to unlabeled audio data. In this short article, I present the value and of extending DDSP, initially developed for speech and music processing, to avian bioacoustics. The main two challenges reside in the definition of a suitable decoder and learning objective. I review some prior publications in biomechanical models of vocal production for passerines, similarity computing, and differentiable solvers of ordinary differential equations. Together, these publications hint at the feasibility of a fully automated and unsupervised algorithm for biologically plausible resynthesis of birdsong.