  The existing formulations of the Schr\"{o}dinger interpolating dynamics,
which is constrained by the prescribed input-output statistics data, utilize
strictly positive Feynman-Kac kernels. This implies that the related Markov
diffusion processes admit vanishing probability densities only at the
boundaries of the spatial volume confining the process. We extend the framework
to encompass singular potentials and associated nonnegative Feynman-Kac-type
kernels. It allows to deal with general nonnegative solutions of the
Schr\"{o}dinger boundary data problem. The resulting stochastic processes are
capable of both developing and destroying nodes (zeros) of probability
densities in the course of their evolution.
