Probabilistic models for sequential data are the basis for a variety of applications concerned with processing timely ordered information. The predominant approach in this domain is given by recurrent neural networks, implementing either a transformative approach (e.g. Variational Autoencoders or Generative Adversarial Networks) or a regression-based approach, i.e. variations of Mixture Density networks (MDN). While these approaches effectively approximate complex probability distributions over full trajectories, their respective output distributions fall short in terms of post-hoc inference capabilities. To overcome this limitation, we extend on an MDN variant, which parameterizes (mixtures of) probabilistic Bézier curves ( \(\mathcal {N}\) -Curves), allowing us to establish a connection to the framework of Gaussian processes. For this, we show that \(\mathcal {N}\) -Curves are a special case of non-stationary Gaussian processes (denoted as \(\mathcal {N}\) -GP) and then derive corresponding mean and kernel functions for different modalities. Then, we propose the use of this MDN variant as a data-dependent generator for \(\mathcal {N}\) -GP prior distributions, resulting in a novel probabilistic trajectory prediction model that inherently supports post-hoc Bayesian inference. We show the advantages granted by this combined prediction model in the context of long-term human trajectory prediction.