  In open-domain dialogue generation tasks, contexts and responses in most
datasets are one-to-one mapped, violating an important many-to-many
characteristic: a context leads to various responses, and a response answers
multiple contexts. Without such patterns, models poorly generalize and prefer
responding safely. Many attempts have been made in either multi-turn settings
from a one-to-many perspective or in a many-to-many perspective but limited to
single-turn settings. The major challenge to many-to-many augment multi-turn
dialogues is that discretely replacing each turn with semantic similarity
breaks fragile context coherence. In this paper, we propose DialoGue Path
Sampling (DialoGPS) method in continuous semantic space, the first many-to-many
augmentation method for multi-turn dialogues. Specifically, we map a dialogue
to our extended Brownian Bridge, a special Gaussian process. We sample latent
variables to form coherent dialogue paths in the continuous space. A dialogue
path corresponds to a new multi-turn dialogue and is used as augmented training
data. We show the effect of DialoGPS with both automatic and human evaluation.
