Multilingual neural machine translation models typically handle one source language at a time. However, prior work has shown that translating from multiple source languages improves translation quality. Different from existing approaches on multi-source translation that are limited to the test scenario where parallel source sentences from multiple languages are available at inference time, we propose to improve multilingual translation in a more common scenario by exploiting synthetic source sentences from auxiliary languages. We train our model on synthetic multi-source corpora and apply random masking to enable flexible inference with single-source or bi-source inputs. Extensive experiments on Chinese/English-Japanese and a large-scale multilingual translation benchmark show that our model outperforms the multilingual baseline significantly by up to +4.0 BLEU with the largest improvements on low-resource or distant language pairs.