# CycleDiffusion: Voice Conversion Using Cycle-Consistent Diffusion Models
## 5 Conclusions  
DMs have emerged as a promising approach in the field of voice conversion, leveraging their ability to generate high-quality, diverse data through a two-phase process of forward diffusion and reverse denoising. They ensure stability and quality in data generation compared to traditional methods such as VAEs and GANs. Although DMs for voice conversion have shown substantial potential, conventional DM-based voice conversion methods only learn the reconstruction path, similar to VAEs, and fail to learn the conversion path, leaving much room for improvement in the converted speech quality. To address this, we have proposed CycleDiffusion, which leverages cycle consistency loss for training DMs. The proposed approach aims to learn both the reconstruction and conversion paths, while ensuring that linguistic information remains unchanged.  
Both objective and subjective evaluations confirmed that the proposed method significantly enhanced the quality of the transformed speech. In the objective assessment of the speaker similarity, CycleDiffusion achieved an improvement ranging from 10.8% to 38.7%. In the objective evaluation of linguistic information retention, it realized a 10.8% error reduction in speech recognition. During the traditional MCD assessment, it noted a 15.9% enhancement. Finally, in the subjective assessment conducted using MOSNet, the proposed method demonstrated a 5.7% increase in the average MOS value and a 32.1% reduction in the confidence interval.  
The time complexity of training the proposed method grows quadratically with respect to the number of training speakers. To reduce the computational burden, we used a subset of each batch when training the conversion paths. In future research, we plan to analyze the trade-off between the amount of data used for conversion path training and the resulting voice conversion performance, aiming to develop an efficient conversion path training strategy. Additionally, another future direction could be integrating cycle consistency loss into a hybrid model that combines DM and GAN.  
Conceptualization, methodology, and writing--original draft preparation, D.Y.; experiment, G.H. (while he was a student at Artificial Intelligence Laboratory in Korea University), H.-P.C. and I.-C.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1E1A1A01078157). Also, it was supported by the NRF under project BK21 FOUR.  
Not applicable.  
Figure 2: Sample spectrograms of the converted utterances using DiffVC and CycleDiffusion: (**a**) an example where the MOS score of the utterance processed by CycleDiffusion is higher than that of DiffVC; (**b**) an example where the MOS score of the utterance processed by CycleDiffusion is lower than that of DiffVC.  
Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.