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A cascaded speech translation model relies on discrete and non-differentiable transcription, which provides a supervision signal from the source side and helps the transformation between source speech and target text. Such modeling suffers from error propagation between ASR and MT models. Direct speech translation is an alternative method to avoid error propagation; however, its performance is often behind the cascade system. To use an intermediate representation and preserve the end-to-end trainability, previous studies have proposed using two-stage models by passing the hidden vectors of the recognizer into the decoder of the MT model and ignoring the MT encoder. This work explores the feasibility of collapsing the entire cascade components into a single end-to-end trainable model by optimizing all parameters of ASR and MT models jointly without ignoring any learned parameters. It is a tightly integrated method that passes renormalized source word posterior distributions as a soft decision instead of one-hot vectors and enables backpropagation. Therefore, it provides both transcriptions and translations and achieves strong consistency between them. Our experiments on four tasks with different data scenarios show that the model outperforms cascade models up to 1.8% in BLEU and 2.0% in TER and is superior compared to direct models.