Large Language Models (LLMs) have recently garnered significant attention, primarily for their capabilities in text-based interactions. However, natural human interaction often relies on speech, necessitating a shift towards voice-based models. A straightforward approach to achieve this involves a pipeline of ``Automatic Speech Recognition (ASR) + LLM + Text-to-Speech (TTS)", where input speech is transcribed to text, processed by an LLM, and then converted back to speech. Despite being straightforward, this method suffers from inherent limitations, such as information loss during modality conversion and error accumulation across the three stages. To address these issues, Speech Language Models (SpeechLMs) -- end-to-end models that generate speech without converting from text -- have emerged as a promising alternative. This survey paper provides the first comprehensive overview of recent methodologies for constructing SpeechLMs, detailing the key components of their architecture and the various training recipes integral to their development. Additionally, we systematically survey the various capabilities of SpeechLMs, categorize the evaluation metrics for SpeechLMs, and discuss the challenges and future research directions in this rapidly evolving field.

Neural text-to-speech systems are often optimized on L1/L2 losses, which make strong assumptions about the distributions of the target data space. Aiming to improve those assumptions, Normalizing Flows and Diffusion Probabilistic Models were recently proposed as alternatives. In this paper, we compare traditional L1/L2-based approaches to diffusion and flow-based approaches for the tasks of prosody and mel-spectrogram prediction for text-to-speech synthesis. We use a prosody model to generate log-f0 and duration features, which are used to condition an acoustic model that generates mel-spectrograms. Experimental results demonstrate that the flow-based model achieves the best performance for spectrogram prediction, improving over equivalent diffusion and L1 models. Meanwhile, both diffusion and flow-based prosody predictors result in significant improvements over a typical L2-trained prosody models.