  Representations of sequential data are commonly based on the assumption that
observed sequences are realizations of an unknown underlying stochastic
process, where the learning problem includes determination of the model
parameters. In this context the model must be able to capture the multi-modal
nature of the data, without blurring between modes. This property is essential
for applications like trajectory prediction or human motion modeling. Towards
this end, a neural network model for continuous-time stochastic processes
usable for sequence prediction is proposed. The model is based on Mixture
Density Networks using B\'ezier curves with Gaussian random variables as
control points (abbrev.: $\mathcal{N}$-Curves). Key advantages of the model
include the ability of generating smooth multi-mode predictions in a single
inference step which reduces the need for Monte Carlo simulation, as required
in many multi-step prediction models, based on state-of-the-art neural
networks. Essential properties of the proposed approach are illustrated by
several toy examples and the task of multi-step sequence prediction. Further,
the model performance is evaluated on two real world use-cases, i.e. human
trajectory prediction and human motion modeling, outperforming different
state-of-the-art models.
