# MixDiff-TTS: Mixture Alignment and Diffusion Model for Text-to-Speech
## 2 Materials and Methods
### Background
#### 2.1.2 HiFi-GAN Vocoder  
A vocoder is a system used for analyzing and synthesizing speech signals. As a key component of speech synthesis systems, its performance directly determines the naturalness and clarity of synthesized speech. Early neural vocoders, such as WaveNet [11] and WaveGlow [27], can convert the acoustic features predicted by acoustic models into audio waveforms. However, these vocoders have several issues [28; 29]. First, WaveNet generates audio in an autoregressive manner (i.e., sequentially by time steps). Its sequential generation nature leads to slow inference speed and low real-time performance. Second, the core of WaveGlow is invertible neural networks, which directly model data distributions through latent variable transformations. However, its complex structural design results in high training costs.  
To address these issues, [PERSON] et al. proposed the HiFi-GAN vocoder based on the Generative Adversarial Network (GAN). Its architecture consists of two core components: a generator and a discriminator. The generator uses transposed convolutions to perform multi-scale upsampling on the mel-spectrogram and innovatively introduces the Multi-Receptive Field Fusion (MRF) module. The MRF module captures multi-time-scale features of the speech signal by stacking residual blocks with different convolutional kernel sizes in parallel. The discriminator is composed of a Multi-Scale Discriminator (MSD) and a Multi-Period Discriminator (MPD). The MSD extracts features at different scales through multiple average pooling operations. The MPD uses two-dimensional convolutions to capture the periodic features of the audio. Leveraging the unique structures of the generator and the discriminator, HiFi-GAN can generate high-fidelity speech in real time. Compared with early neural vocoders, HiFi-GAN has three significant advantages [19]. First, it achieves efficient inference through a non-autoregressive architecture. In terms of inference speed, HiFi-GAN is approximately seven times faster than WaveGlow and significantly outperforms WaveNet. Second, it adopts a lightweight network structure. The number of parameters in HiFi-GAN is only half that of WaveNet and one-sixth that of WaveGlow, reducing the demand for computational resources. Third, through the MRF module and dual discriminators, HiFi-GAN can generate high-fidelity speech. In the MOS evaluation, HiFi-GAN improves by 0.34 points compared to WaveNet and 0.55 points compared to WaveGlow.  
Additionally, as research on diffusion models has deepened, a diffusion-model-based vocoder has emerged (e.g., DiffWave [30]). This type of vocoder gradually converts random noise into high-quality audio by introducing diffusion models. However, since generating audio with diffusion models requires dozens to hundreds of iterations, their inference speed is slow. In contrast, HiFi-GAN can map all input features into an audio waveform at once, so it has high real-time performance [31]. In real-time speech synthesis scenarios, HiFi-GAN leverages the efficient architecture of the MRF module to generate high-fidelity speech comparable to diffusion-based vocoders, without sacrificing inference speed. Therefore, we select HiFi-GAN as the vocoder for MixDiff-TTS.