  Open-domain question answering (QA) systems are often built with retrieval
modules. However, retrieving passages from a given source is known to suffer
from insufficient knowledge coverage. Alternatively, prompting large language
models (LLMs) to generate contextual passages based on their parametric
knowledge has been shown to improve QA performance. Yet, LLMs tend to
"hallucinate" content that conflicts with the retrieved knowledge. Based on the
intuition that answers supported by both sources are more likely to be correct,
we propose COMBO, a Compatibility-Oriented knowledge Merging for Better
Open-domain QA framework, to effectively leverage the two sources of
information. Concretely, we match LLM-generated passages with retrieved
counterparts into compatible pairs, based on discriminators trained with silver
compatibility labels. Then a Fusion-in-Decoder-based reader model handles
passage pairs to arrive at the final answer. Experiments show that COMBO
outperforms competitive baselines on three out of four tested open-domain QA
benchmarks. Further analysis reveals that our proposed framework demonstrates
greater efficacy in scenarios with a higher degree of knowledge conflicts.
