Weaknesses: I was a little confused about how the grouped 1x1 convolutions interact with the coupling layers. If the standard (half-and-half) partitioning is used for the coupling layers and the grouped 1x1 convolutions never mix channels outside of their group of 4, then half of the channels will never be transformed by any coupling layer. I'm assuming the authors deal with this issue somehow (since the results are good), but I only briefly scanned the code and didn't want to work through all of the index gymnastics. I could see readers being confused by these missing details. Update: In their response, the authors said they will explain more of the details of the grouped 1x1 convolutions in their revised version.

After rebuttal and discussion, all four reviewers provide very favorable reviews. The reviewers point out a novel methodology, combining flows with dynamic programming (hard monotonic alignment). The paper is therefore accepted for an oral.

Recently, text-to-speech (TTS) models such as FastSpeech and ParaNet have been proposed to generate mel-spectrograms from text in parallel. Despite the advantage, the parallel TTS models cannot be trained without guidance from autoregressive TTS models as their external aligners. In this work, we propose Glow-TTS, a flow-based generative model for parallel TTS that does not require any external aligner. By combining the properties of flows and dynamic programming, the proposed model searches for the most probable monotonic alignment between text and the latent representation of speech on its own. We demonstrate that enforcing hard monotonic alignments enables robust TTS, which generalizes to long utterances, and employing generative flows enables fast, diverse, and controllable speech synthesis.

Monotonic alignment search (MAS), introduced by Glow-TTS, is one of the most popular algorithm in TTS to estimate unknown alignments between text and speech. Since this algorithm needs to search for the most probable alignment with dynamic programming by caching all paths, the time complexity of the algorithm is $O(T \times S)$. The authors of Glow-TTS run this algorithm on CPU, and while they mentioned it is difficult to parallelize, we found that MAS can be parallelized in text-length dimension and CPU execution consumes an inordinate amount of time for inter-device copy. Therefore, we implemented a Triton kernel and PyTorch JIT script to accelerate MAS on GPU without inter-device copy. As a result, Super-MAS Triton kernel is up to 72 times faster in the extreme-length case. The code is available at \url{https://github.com/supertone-inc/super-monotonic-align}.