# SGM-EMA: Speech Enhancement Method Score-Based Diffusion Model and EMA Mechanism
## 2 Methodology
### Numerical SDE Solver
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment Number** & **Model A** & **Model B** & **Model C** & **PESQ (\(\uparrow\))** & **ESTOI (\(\uparrow\))** & **SI-SDR (\(\uparrow\))** \\ \hline
1 & \(\times\) & \(\times\) & \(\times\) & 2.12 \(\pm\) 0.49 & 0.76 \(\pm\) 0.09 & 12.8 \(\pm\) 4.1 \\
2 & \(\times\) & \(\times\) & \(\surd\) & 2.24 \(\pm\) 0.51 & 0.80 \(\pm\) 0.09 & 14.1 \(\pm\) 4.0 \\
3 & \(\surd\) & \(\times\) & \(\times\) & 2.57 \(\pm\) 0.65 & 0.78 \(\pm\) 0.10 & 16.3 \(\pm\) 3.7 \\
4 & \(\surd\) & \(\times\) & \(\surd\) & 2.69 \(\pm\) 0.63 & 0.86 \(\pm\) 0.10 & 17.3 \(\pm\) 3.5 \\
5 & \(\times\) & \(\surd\) & \(\times\) & 2.72 \(\pm\) 0.63 & 0.85 \(\pm\) 0.10 & 16.6 \(\pm\) 3.1 \\
6 & \(\times\) & \(\surd\) & \(\surd\) & 2.89 \(\pm\) 0.80 & 0.91 \(\pm\) 0.07 & 19.6 \(\pm\) 3.5 \\ \hline \hline \end{tabular} \(\uparrow\): indicates that a higher value corresponds to better performance.

\end{table} 
Table 4: Ablation study results on the VB-DMD dataset. (Model A: Euler–Maruyama method; Model B: reverse diffusion method; Model C: EMA mechanism). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment Number** & **Model A** & **Model B** & **Model C** & **PESQ (\(\uparrow\))** & **ESTOI (\(\uparrow\))** & **SI-SDR (\(\uparrow\))** \\ \hline
1 & \(\times\) & \(\times\) & \(\times\) & 1.74 \(\pm\) 0.40 & 0.72 \(\pm\) 0.11 & 11.2 \(\pm\) 4.1 \\
2 & \(\times\) & \(\times\) & \(\surd\) & 1.81 \(\pm\) 0.44 & 0.75 \(\pm\) 0.12 & 12.1 \(\pm\) 4.4 \\
3 & \(\surd\) & \(\times\) & \(\times\) & 2.40 \(\pm\) 0.56 & 0.71 \(also exhibited lower variance, demonstrating remarkable stability. These results not only verify the outstanding performance of SGM-EMA in speech enhancement tasks but also statistically confirm its reliability, establishing a solid foundation for further advancements in speech enhancement technology. When the training and testing datasets were mismatched--that is, when the models were trained on the VB-DMD dataset and evaluated on the TIMIT-TUT dataset--we evaluated model performance under these mismatch conditions. We tested the TIMIT-TUT data using pretrained models provided in the official codebases of the respective papers. The experimental results are summarized in Table 7. To provide a more intuitive comparison, the average values of each metric in Table 7 are visualized in Figure 5b. As expected, the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Type** & **Training Set** & **Test Set** & **PESQ (\(\uparrow\))** & **ESTOI (\(\uparrow\))** & **SI-SDR (\(\uparrow\))** \\ \hline MetricGAN+ [62] & D & VB-DMD & VB-DMD & 3.13 \(\pm\) 0.55 (\(\pm\)0.68) & 0.83 \(\pm\) 0.11 (\(\pm\)0.14) & 8.5 \(\pm\) 3.6 (\(\pm\)4.5) \\ SERGAN [63] & D & VB-DMD & VB-DMD & 2.62 \(\pm\) 0.63 (\(\pm\)0.78) & 0.85 \(\pm\) 0.06 (\(\pm\)0.08) & 17.2 \(\pm\) 3.2 (\(\pm\)4.0) \\ CMGAN [64] & D & VB-DMD & VB-DMD & 3.41 \(\pm\) 0.68 (\(\pm\)0.84) & 0.88 \(\pm\) 0.10 (\(\pm\)0.12) & 18.4 \(\pm\) 4.2 (\(\pm\)5.2) \\ RVAE [65] & G & VB & VB-DMD & 2.48 \(\pm\) 0.55 (\(\pm\)0.68) & 0.81 \(\pm\) 0.11 (\(\pm\)0.14) & 17.1 \(\pm\) 5.0 (\(\pm\)6.2) \\ CDiffuse [66] & G & VB-DMD & VB-DMD & 2.46 \(\pm\) 0.51 (\(\pm\)0.63) & 0.79 \(\pm\) 0.11 (\(\pm\)0.14) & 12.6 \(\pm\) 5.0 (\(\pm\)6.2) \\ SGM-EMA [ours] & G & VB-DMD & VB-DMD & 2.89 \(\pm\) 0.80 (\(\pm\)0.99) & 0.91 \(\pm\) 0.07 (\(\pm\)0.09) & 19.6 \(\pm\) 3.5 (\(\pm\)4.3) \\ \hline \hline \end{tabular} \(\uparrow\): indicates that a higher value corresponds to better performance.

\end{table} 
Table 6: Under matched evaluation conditions, the results in this table are categorized by model types D and G. Except for SGM-EMA and SERGAN, all methods used pre-trained models published in their original papers and were evaluated on the same test set (VB-DMD) with five independent runs. The data in the table are presented as the means \(\pm\) standard deviations (95% confidence interval). Figure 5: **(a)** The data from Table 6 [60; 61; 62; 63; 64; 65; 66]; (b) the data from Table 7 [60; 61; 62; 63; 64; 65; 66].