# SGM-EMA: Speech Enhancement Method Score-Based Diffusion Model and EMA Mechanism
## 2 Methodology
### Numerical SDE Solver
The input and output layers use Conv2D layers with 3 \(\times\) 3 convolution kernels and a stride of 1. The residual block structure derived from the BigGAN architecture [53] is embedded in both the downsampling and upsampling blocks. Each residual block consists of the same Conv2D layer as above, group normalization [54], LeakyReLU activation function, and either upsampling or downsampling layers based on finite impulse response (FIR) filters [55]. Each downsampling path contains two residual blocks, and each upsampling path contains three residual blocks [56]. A 1 \(\times\) 1 Conv2D layer is employed to facilitate the progressive transformation of feature dimensionality [57]. The network performs symmetrical dimensionality reduction and expansion through feature maps of specific resolutions. The output dimensions of the downsampling paths are (256, 256, 128), (128, 128, 128), (64, 64, 256), (32, 32, 256), (16, 16, 256), (8, 8, 256), and (4, 4, 256). To enhance feature fusion, an EMA mechanism is added to the bottleneck layer and the 16 \(\times\) 16 and 64 \(\times\) 64 resolution layers. The overall architecture supports efficient gradient propagation and multi-scale feature aggregation through the combination of residual connections and attention mechanisms, showing significant performance advantages in speech enhancement tasks. To enhance the model's temporal perception, we used Fourier embeddings [58] to map the time scalar \(t\) into an m-dimensional vector \(t_{emb}\). Fourier transform was then applied to encode temporal information into a representation suitable for neural network processing. This vector was embedded into each residual block, as shown in Figure 4, so that the model could simultaneously consider the interaction between temporal dynamics and spatial features. This temporal encoding mechanism not only allowed the network to model

Figure 3: U-Net basic structure diagram. [[https://doi.org/10.7488/ds/2117](https://doi.org/10.7488/ds/2117)]([https://doi.org/10.7488/ds/2117](https://doi.org/10.7488/ds/2117)), accessed on 10 September 2024). The clean speech signal came from the VoiceBank dataset, with a sampling rate of 48 kHz, and the noisy signal came from the DEMAND dataset, with a sampling rate of 48 kHz. The dataset contains a variety of real-world background noises, such as cafes, streets, and offices. The training set (11,572 utterances) consisted of 28 speakers with signal-to-noise ratios (SNRs) of 15, 10, 5, and 0 dB. The test set (824 utterances) consisted of 2 speakers with SNRs of 17.5, 12.5, 7.5, and 2.5 dB. Both the training and test sets were resampled to 16 kHz. 2. TIMIT-TUT: The TIMIT-TUT dataset was created by selecting the complete test set of the acoustic-phonetic continuous speech corpus jointly constructed by Texas Instruments (TI), Massachusetts Institute of Technology (MIT), and Stanford Research Institute (SRI), and the noise signal from TUT. The TUT noise dataset covers a variety of sound events in daily environments, such as traffic noise, human voices, animal calls, etc. (it is available at [[https://paperswithcode.com/dataset/tut-sound-events-2017](https://paperswithcode.com/dataset/tut-sound-events-2017)]([https://paperswithcode.com/dataset/tut-sound-events-2017](https://paperswithcode.com/dataset/tut-sound-events-2017)), accessed on 13 September 2024). The TIMIT [60] complete test set of clean speech consists of 1344 utterances spoken by 168 speakers with a sampling rate of 16 kHz (it is available at [[https://goo.gl/l0](https://goo.gl/l0) sPwz]([https://goo.gl/l0](https://goo.gl/l0) sPwz), accessed on 14 September 2024). The TIMIT-TUT mixed dataset was a random segment from a noise file randomly selected from the noise signal and added to the clean speech signal, generating a total of 1344 mixed speech samples for testing. All mixed datasets were resampled uniformly to 16 kHz, with a signal-to-noise ratio between 0 and 20 dB.