  Large water Cherenkov detectors have shaped our current knowledge of neutrino
physics and nucleon decay, and will continue to do so in the foreseeable
future. These highly capable detectors allow for directional and topological,
as well as calorimetric information to be extracted from signals on their
photosensors. The current state-of-the-art approach to water Cherenkov
reconstruction relies on maximum-likelihood estimation, with several
simplifying assumptions employed to make the problem tractable. In this paper,
we describe neural networks that produce probability density functions for the
signals at each photosensor, given a set of inputs that characterizes a
particle in the detector. The neural networks we propose allow for
likelihood-based approaches to event reconstruction with significantly fewer
assumptions compared to traditional methods, and are thus expected to improve
on the current performance of water Cherenkov detectors.
