## 1 Introduction  
Voice conversion (VC) aims to modify the speech signal spoken by a source speaker to make it sound as if it was spoken by a different speaker, referred to as the target speaker while keeping the linguistic content unchanged. VC has a wide range of applications, including personalized speech synthesis, speech enhancement, speaker identification, human-robot interaction, and movie dubbing. Generally, voice conversion systems differ in terms of how the datasets are obtained and utilized during training. Systems using parallel training data require recordings of the same linguistic content from paired source and target speakers, while those using non-parallel training data (i.e., non-parallel VC) are trained on unpaired speech data. A recent comprehensive overview of VC techniques and their performance evaluation methods, from statistical approaches to deep learning, can be found in [1, 2]. Various methods have been proposed for parallel voice conversion tasks using statistical modeling, such as Gaussian Mixture Models (GMMs) [3, 4] and frequency warping [5, 6]. Although these methods are low-cost in terms of time and resources, spectral details are typically lost when using low-dimensional representations, leading to overly smoothed speech waveforms. To overcome this issue, more advanced models have been developed, taking advantage of machine learning-based techniques such as Deep Neural Networks (DNNs) [7, 8], Recurrent Neural Networks (RNNs) [9] and Sequence-To-Sequence (Seq2 Seq) [10, 11], which achieved superior performance in terms of naturalness and similarity when compared to conventional VC methods [2]. While previous VC methods have shown promising outcomes, they face a significant limitation: the requirement for parallel training data, which may not always be readily available in practice. In recent years, VC research utilizing non-parallel training data has seen substantial improvements, largely due to the effectiveness of deep learning techniques in learning mapping functions. Successful techniques have been developed, such as those in [12, 13, 14, 15]. For example, approaches including CyleGAN-VC [16, 17], StarGAN-VC [18, 19] and VAWGAN [20, 21], have employed generative adversarial networks (GANs) [22] to improve both speech quality and similarity to the target speaker, particularly when a large amount of speech data is available. Other approaches, introduced in [13, 15], use Seq2 Seq models and aim to separate linguistic features from speaker identity components. During the training process, the model learns linguistic representations from acoustic features using the encoder output as the reference. At run-time conversion, the Seq2 Seq decoder is used to reconstruct the acoustic features, taking advantage of target speaker representations. The recent advances in non-parallel VC involve the use of linguistic features extracted from the automatic speech recognition (ASR) model trained using a large multi-speaker corpus, such as Phonetic PosteriorGram (PPG) and bottleneck features. PPGs refer to frame-level contextual representations derived from the posterior probabilities associated with each phonetic class, using a speaker-independent ASR system (SI-ASR). The application of these techniques has received particular attention in relevant studies [10, 23, 24, 25, 26] where a conversion model is first used to convert PPGs extracted from the source speech into spectral features of the target speaker. Subsequently, a vocoder is applied using the converted features to generate the target speaker's speech waveforms. WaveNet [24] serves as the primary neural vocoder widely utilized in VC methods. However, it has a limitation in generating only one speech sample at a time, which presents challenges for real-time applications. Moreover, despite the success of PPGs, one of their limitations is the lack of smoothness in the trajectory of the generated waveforms, leading to speech artifacts, particularly in run-time conversion.