# SGM-EMA: Speech Enhancement Method Score-Based Diffusion Model and EMA Mechanism
## 2 Methodology
### Numerical SDE Solver
### Hyperparameter Configuration

The hyperparameters in Equations (2) and (7) were set to \(\sigma_{min}=0.05\), \(\sigma_{max}=0.5\), and \(\gamma=1.5\). The Adam optimizer was used for training, the learning rate was set to \(10^{-4}\), and the batch size was 8. The exponential moving average decay rate of the model weight was 0.999, which was used for sampling [61], and the sampler used the PC sampler. The number of backward steps in the SDE was set to N = 30 [56], and the step size r of the annealing Langevin dynamics in the corrector was set to 0.5. The U-Net network had 14 layers (7 layers for the encoder and 7 layers for the decoder). The resolution and number of channels of the encoder and decoder were symmetrical. We show the number of channels and resolution of the encoder in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Encoder Layers** & **Resolution** & **Channels** & **Normalization** \\ \hline
1 & 256 \(\times\) 256 & 128 & \\
2 & 128 \(\times\) 128 & 128 & \\
3 & 64 \(\times\) 64 & 256 & \\
4 & 32 \(\times\) 32 & 256 & Group normalization \\
5 & 16 \(\times\) 16 & 256 & \\
6 & 8 \(\times\) 8 & 256 & \\
7 & 4 \(\times\) 4 & 256 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: U-Net encoder layer parameter table. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Specific Configuration** \\ \hline Operating System & Linux-5.15.0-86-generic-x86\_64-with-glibc2.35 \\ Processor & NVIDIA vGPU-32 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental configuration table. ### Baseline

We compared the proposed method with three discriminative baselines (MetricGAN+ [62], SERGAN [63], and CMGAN [64]) and two generative baselines (RVAE [65] and Cliffwise [66]). All methods utilized the pre-trained models provided in the publicly available code from the corresponding papers to evaluate the datasets. Except for the SERGAN method, we retrained the models from scratch on the VB-DMD dataset and then evaluated them on both the VB-DMD and TIMIT-TUT datasets. ### Evaluation Metrics

To evaluate the performance of the proposed method, three objective metrics were adopted: PESQ [67], ESTOI [68], and SI-SDR [69]. 1. PESQ: This metric assesses perceptual speech quality and is commonly used in voice communication and speech enhancement. It produces scores ranging from \(-0.5\) to \(4.5\), where a higher score indicates better speech quality and a lower score indicates poor speech quality. 2. ESTOI: This is an objective indicator for evaluating speech intelligibility in speech enhancement systems. ESTOI provides scores between 0 and 1, where values closer to 1 indicate better speech intelligibility, and values closer to 0 indicate poorer speech intelligibility. 3. SI-SDR: This metric evaluates signal reconstruction accuracy in tasks such as speech enhancement, denoising, and source separation. Values below 10 dB suggest significant distortion and poor reconstruction, scores between 10 and 20 dB indicate acceptable quality with moderate artifacts, and values above 20 dB imply high-fidelity reconstruction with minimal distortion or noise. ### Ablation Study

To evaluate the effectiveness of the Euler-Maruyama method and the reverse diffusion method in the predictor component of the PC sampler, as well as the contribution of the EMA mechanism to the performance of the speech enhancement model, we conducted a series of ablation studies. By selectively disabling or replacing key components of the predictor and the EMA module, we compared multiple model configurations on the VB-DMD and TIMIT-TUT datasets. The results, presented in Tables 4 and 5 as the means \(\pm\) standard deviations, demonstrate that the reverse diffusion method was more effective than the Euler-Maruyama method, and that the inclusion of the EMA mechanism further improved the overall model performance.