  This paper describes several improvements to a new method for signal
decomposition that we recently formulated under the name of Differentiable
Dictionary Search (DDS). The fundamental idea of DDS is to exploit a class of
powerful deep invertible density estimators called normalizing flows, to model
the dictionary in a linear decomposition method such as NMF, effectively
creating a bijection between the space of dictionary elements and the
associated probability space, allowing a differentiable search through the
dictionary space, guided by the estimated densities. As the initial formulation
was a proof of concept with some practical limitations, we will present several
steps towards making it scalable, hoping to improve both the computational
complexity of the method and its signal decomposition capabilities. As a
testbed for experimental evaluation, we choose the task of frame-level piano
transcription, where the signal is to be decomposed into sources whose activity
is attributed to individual piano notes. To highlight the impact of improved
non-linear modelling of sources, we compare variants of our method to a linear
overcomplete NMF baseline. Experimental results will show that even in the
absence of additional constraints, our models produce increasingly sparse and
precise decompositions, according to two pertinent evaluation measures.
