  Sequence-to-sequence automatic speech recognition (ASR) models require large
quantities of data to attain high performance. For this reason, there has been
a recent surge in interest for unsupervised and semi-supervised training in
such models. This work builds upon recent results showing notable improvements
in semi-supervised training using cycle-consistency and related techniques.
Such techniques derive training procedures and losses able to leverage unpaired
speech and/or text data by combining ASR with Text-to-Speech (TTS) models. In
particular, this work proposes a new semi-supervised loss combining an
end-to-end differentiable ASR$\rightarrow$TTS loss with TTS$\rightarrow$ASR
loss. The method is able to leverage both unpaired speech and text data to
outperform recently proposed related techniques in terms of \%WER. We provide
extensive results analyzing the impact of data quantity and speech and text
modalities and show consistent gains across WSJ and Librispeech corpora. Our
code is provided in ESPnet to reproduce the experiments.
