# SGM-EMA: Speech Enhancement Method Score-Based Diffusion Model and EMA Mechanism
## 2 Methodology
### Numerical SDE Solver
In the EMA mechanism, the global spatial information from the \(1\times 1\) convolution branch is processed by applying Softmax activation to generate channel-wise attention weights, while the \(3\times 3\) convolution branch output is reshaped to match the dimensions of the \(1\times 1\) branch. The features from these two branches are then combined through matrix multiplication, leading to the formation of the first spatial attention map. At the same time, a 2D average pooling operation is performed on the \(3\times 3\) branch, and the resulting features are passed through a Softmax function to produce another set of attention weights. Similarly, the \(1\times 1\) branch output is reshaped, and matrix multiplication between the two branches yields the second spatial attention map. To refine the spatial attention distribution, the EMA module aggregates the feature outputs guided by the attention maps from both branches. This design allows the model to exploit complementary spatial features learned in parallel, enhancing its ability to capture richer contextual information. In this way, when the model performs attention calculations, it not only considers the current input features but also effectively integrates contextual information from previous layers. It is particularly worth mentioning that the EMA mechanism adopts a parallel sub-structure design, which effectively avoids excessive sequential processing and eliminates the need for increased network depth. This reduces redundant sequence processing steps and decreases instability during training, thereby improving the overall performance of the model. In addition, the parallelization of convolution operations further strengthens the expressive capacity of the structure. By combining the parallel computing methods of \(3\times 3\) convolution and \(1\times 1\) convolution, the model can simultaneously capture local short-term dependencies and global long-term dependencies, thereby merging more contextual information into the intermediate feature map. The EMA module will be further evaluated through ablation studies in Section 4.5. ### Multi-Resolution U-Net Network

In recent years, significant progress has been made in enhancing acoustic quality through deep learning methods, with the U-Net architecture emerging as a particularly effective model [50; 51]. As illustrated in Figure 3, the U-Net consists of three main components: an encoder, a decoder, and skip connections. Specifically, the encoder progressively downsamples the input audio to extract high-level acoustic representations, while the decoder performs upsampling to reconstruct enhanced audio with dimensions matching the original input. The skip connections directly transfer feature maps from the encoder to the corresponding decoder layers, enabling the integration of low-level and high-level information to facilitate more accurate detail restoration. Some U-Net-based speech enhancement models rely on ordinary convolution operations in the encoder and decoder, which may overlook speech contextual information and result in the loss of detailed features. To address these problems, we incorporated the EMA mechanism into the U-Net-based network. This approach focuses on the detailed speech features, extracts local features at different scales, and captures more contextual information, thereby enabling more effective speech enhancement. Figure 2: EMA mechanism module structure diagram. ## 3 Network Model Structure

The SGM-EMA model is built on the Noise Conditional Score Network++ (NCSN++) architecture [41] and uses a multi-resolution U-Net-based structure. Previous studies [52] have shown that this type of structure has strong capabilities in tasks such as generation and segmentation. In Figure 4, we show feature maps at different resolutions, annotate their spatial sizes and number of channels, and use arrows to illustrate the transformations between feature maps. The main body of the network consists of symmetrical downsampling and upsampling paths, along with skip connections.