  Developing text-based robot trajectory generation models is made particularly
difficult by the small dataset size, high dimensionality of the trajectory
space, and the inherent complexity of the text-conditional motion distribution.
Recent manifold learning-based methods have partially addressed the
dimensionality and dataset size issues, but struggle with the complex
text-conditional distribution. In this paper we propose a text-based trajectory
generation model that attempts to address all three challenges while relying on
only a handful of demonstration trajectory data. Our key idea is to leverage
recent flow-based models capable of capturing complex conditional
distributions, not directly in the high-dimensional trajectory space, but
rather in the low-dimensional latent coordinate space of the motion manifold,
with deliberately designed regularization terms to ensure smoothness of motions
and robustness to text variations. We show that our {\it Motion Manifold Flow
Primitive (MMFP)} framework can accurately generate qualitatively distinct
motions for a wide range of text inputs, significantly outperforming existing
methods.
