In this paper, we conduct the first study on spurious correlations for open-domain response generation models based on a corpus CGDialog curated by ourselves. The current models indeed suffer from spurious correlations and have a tendency to generate irrelevant and generic responses. Inspired by causal discovery algorithms, we propose a novel model-agnostic method for training and inference using a conditional independence classifier. The classifier is trained by a constrained self-training method, coined ConSTrain , to overcome data sparsity. The experimental results based on both human and automatic evaluation show that our method significantly outperforms the competitive baselines in terms of relevance, informativeness, and fluency.