Although existing neural retrieval models reveal promising results when training data is abundant and the performance keeps improving as training data increases, collecting high-quality annotated data is prohibitively costly. To this end, we introduce a novel noisy self-training framework combined with synthetic queries, showing that neural retrievers can be improved in a self-evolution manner with no reliance on any external models. Experimental results show that our method improves consistently over existing methods on both general-domain (e.g., MS-MARCO) and out-of-domain (i.e., BEIR) retrieval benchmarks. Extra analysis on low-resource settings reveals that our method is data efficient and outperforms competitive baselines, with as little as 30% of labelled training data. Further extending the framework for reranker training demonstrates that the proposed method is general and yields additional gains on tasks of diverse domains.\footnote{Source code is available at \url{https://github.com/Fantabulous-J/Self-Training-DPR}}
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