Title: End-to-End Speech Synthesis Based on Deep Conditional Schrödinger Bridges. Abstract:   Speech synthesis plays an important role in human-computer interaction. Existing methods mainly employ traditional two-stage pipeline, e.g. text-to-speech and vocoder. In this paper, we propose a system called Schr\"on, which can generate speech waves in an end-to-end mamaner by solving Schr\"odinger bridge problems (SBP). In order to make SBP suitable for speech synthesis, we generalize SBP from two aspects. The first generalization makes it possible to accept condition variables, which are used to control the generated speech, and the second generalization allows it to handle variable-size input. Besides these two generalizations, we propose two techniques to fill the large information gap between text and speech waveforms for generating high-quality voice. The first technique is to use a text-mel joint representation as the conditional input of the conditional SBP. The second one is to use a branch network for the generation of mel scores as a regularization, so that the text features will not be degenerated. Experimental results show that Schr\"on achieves state-of-the-art MOS of 4.52 on public data set LJSpeech. Audio samples are available at https://schron.github.io/.