# CycleDiffusion: Voice Conversion Using Cycle-Consistent Diffusion Models
## 4 Experiments
### Objective Evaluation
#### 4.1.3 Mel-Cepstral Distance Test  
For the last metric of objective evaluation, we used the mel-cepstral distance (MCD) [36] as a quantification of the dissimilarity between the converted speech and the target speech. To compensate for the length discrepancies between the converted and target speeches, dynamic time warping (DTW) was applied before calculating the MCD. The cosine similarity serves as a measure of similarity, while the speech recognition accuracy assesses the quality of linguistic content preservation, and MCD measures overall similarity. A lower MCD value between the converted and the target speeches indicates better voice conversion performance. Table 3 summarizes the average MCDs along with the corresponding 95% confidence intervals for the converted speeches generated by DiffVC and CycleDiffusion.  
The experimental findings outlined in Table 3 reveal that the proposed CycleDiffusion model surpasses the baseline DiffVC in both intra-gender and inter-gender voice conversion  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **DiffVC** & **CycleDiffusion** \\ \hline ASR & \(71.3\pm 1.4\) & \(74.4\pm 1.4\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average speech recognition accuracies along with the 95% confidence intervals for the speech samples converted by DiffVC (baseline) and CycleDiffusion (proposed).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Conversion Direction**} & \multicolumn{2}{c}{**DiffVC**} & **CycleDiffusion** \\ \hline \multirow{5}{*}{Intra-gender} & F1\(\rightarrow\)F2 & 5.10 \(\pm\) 0.24 & 4.18 \(\pm\) 0.13 \\  & F2\(\rightarrow\)F1 & 7.18 \(\pm\) 0.46 & 6.28 \(\pm\) 0.38 \\  & M1\(\rightarrow\)M2 & 5.25 \(\pm\) 0.20 & 4.52 \(\pm\) 0.17 \\  & M2\(\rightarrow\)M1 & 6.28 \(\pm\) 0.28 & 5.41 \(\pm\) 0.17 \\  & Average & 5.95 \(\pm\) 0.29 & 5.10 \(\pm\) 0.22 \\ \hline \multirow{5}{*}{Inter-gender} & F1\(\rightarrow\)M1 & 6.12 \(\pm\) 0.21 & 4.98 \(\pm\) 0.15 \\  & F1\(\rightarrow\)M2 & 5.16 \(\pm\) 0.20 & 4.32 \(\pm\) 0.13 \\  & F2\(\rightarrow\)M1 & 5.87 \(\pm\) 0.26 & 4.85 \(\pm\) 0.17 \\  & F2\(\rightarrow\)M2 & 4.88 \(\pm\) 0.20 & 4.33 \(\pm\) 0.18 \\  & M1\(\rightarrow\)F1 & 7.10 \(\pm\) 0.38 & 6.49 \(\pm\) 0.42 \\  & M1\(\rightarrow\)F2 & 5.07 \(\pm\) 0.20 & 4.36 \(\pm\) 0.13 \\  & M2\(\rightarrow\)F1 & 7.16 \(\pm\) 0.38 & 6.58 \(\pm\) 0.37 \\  & \(\rightarrow\)M2\(\rightarrow\)F2 & 5.65 \(\pm\) 0.26 & 4.80 \(\pm\) 0.17 \\  & Average & 5.58 \(\pm\) 0.26 & 5.09 \(\pm\) 0.21 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average MCDs along with the 95% confidence intervals for the speech samples converted by DiffVC (baseline) and CycleDiffusion (proposed).  
tasks, making a 15.9% increase in MCD on average. The CycleDiffusion model consistently achieves lower MCD values regardless of conversion directions, indicating improved quality in the converted speech. This decrease in the MCD values highlights the essential role of incorporating cycle consistency loss into the diffusion-based voice conversion framework, significantly improving conversion performance compared to the baseline.