In open-domain dialogue response generation, a dialogue context can be continued with diverse responses, and the dialogue models should capture such one-to-many relations. In this work, we first analyze the training objective of dialogue models from the view of Kullback-Leibler divergence (KLD) and show that the gap between the real world probability distribution and the single-referenced data's probability distribution prevents the model from learning the one-to-many relations efficiently. Then we explore approaches to multi-referenced training in two aspects. Data-wise, we generate diverse pseudo references from a powerful pretrained model to build multi-referenced data that provides a better approximation of the real-world distribution. Model-wise, we propose to equip variational models with an expressive prior, named linear Gaussian model (LGM). Experimental results of automated evaluation and human evaluation show that the methods yield significant improvements over baselines. We will release our code and data in https://github.com/ZHAOTING/dialog-processing.
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