# DIFFBAS: An Advanced Binaural Audio Synthesis Model Focusing on Binaural Differences Recovery
## 3 Experiments and Results
### Experiment Results
#### 3.2.2 Quantitative Evaluation
The color of each position represents the model's IPD error in the corresponding frequency/time pair. A darker color indicates a smaller IPD error. It can be seen that Figure 7a-d(ii) are darker than Figure 7a-d(i), which indicates that DIFFBAS can reduce IPD errors in the entire time-frequency domain. People usually use IPD at lower frequencies for spatial localization because high frequencies \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & \(\mathbf{\mathcal{L_{2}}\times 10^{3}\downarrow}\) & \(\mathbf{Amp\downarrow}\) & \(\mathbf{\mathcal{L_{\textit{pls}}}\downarrow}\) & \(\mathbf{\mathcal{L_{\textit{IPD}}}\downarrow}\) \\ \hline Mono-Mono & 1.340 & 0.063 & 1.564 & 1.472 \\ Avg-Avg & 0.200 & 0.031 & 0.598 & 1.472 \\ Geo-Warp & 0.408 & 0.052 & 1.156 & 1.414 \\ \hline WarpNet [15] & 0.145 & 0.036 & 0.815 & **1.064 \({}^{\dagger}\)** \\ DIFFBAS + WarpNet & **0.033 \({}^{\ast}\)** & **0.018 \({}^{\ast}\)** & **0.358 \({}^{\ast}\)** & **0.834 \({}^{\ast}\)** \\ \hline NFS [16] & 0.163 & 0.040 & 0.869 & 1.250 \\ DIFFBAS + NFS & **0.049 \({}^{\dagger}\)** & **0.018 \({}^{\ast}\)** & **0.431 \({}^{\dagger}\)** & 1.083 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performances of six BAS models on the four evaluation metrics. We reproduced the results using the official codes for WarpNet and NFS. The \(\downarrow\) symbol indicates that the lower the metric, the better the effect. The optimal value of each metric is marked with an asterisk \((\cdot)^{\ast}\) and bolded, and the suboptimal value is marked with a \((\cdot)^{\dagger}\) and bolded. Figure 6: Comparison of IPD(interaural phase difference) at frequencies with peak energy over a two-second period compared to recording audio. The range of IPD is \([-\pi,\pi]\). The blue line represents the changing trend of recording audio, and the red line represents the changing trend of binaural audio synthesized by the model. can cause perceptual confusion. Further observations of Figure 7b,d shows that in the low-frequency band of 0-2000 Hz, DIFFBAS can effectively reduce IPD errors and outliers, which is more in line with human perception characteristics. Other evaluation metrics, such as \(\mathcal{L}_{2}\), \(Amp\), and \(\mathcal{L}_{pls}\), cannot be used alone to evaluate the performance of BAS systems. Take the dummy Avg-Avg system as an example. Its  
Figure 7: IPD error heatmaps of four BAS models in the time-frequency domain. The darker the point, the lower IPD error of the model. (**a**) IPD error heatmap across the entire frequency range. (i) IPD error of WarpNet. (ii) IPD error of DIFFBAS + WarpNet. (**b**) Heat map of IPD error in low-frequency range. (i) IPD error of WarpNet. (ii) IPD error of DIFFBAS + WarpNet. (**c**) IPD error heatmap across the entire frequency range. (i) IPD error of NFS. (ii) IPD error of DIFFBAS + NFS. (**d**) Heat map of IPD error in low-frequency range. (i) IPD error of NFS. (ii) IPD error of DIFFBAS + NFS. performance on the first three metrics has been significantly improved. In Table 4, compared with WarpNet, the values of \(Amp\) and \(\mathcal{L}_{\textit{plb}}\) have been reduced from 0.036 and 0.815 to 0.031 and 0.598, respectively. However, the synthesized audio has no spatial information at all because its left and right channel signals are always the same and listeners cannot use it to localize the sound source. However, the IPD metric can measure such deficiency of spatial information. The IPD error of the Avg-Avg model is 1.472, which is much larger than the IPD error of WarpNet 1.064. As a comparison, the IPD error of DIFFBAS + WarpNet is 0.834, which means the binaural audio synthesized by DIFFBAS + WarpNet provides more accurate spatial information. Similar results are also found when comparing Avg-Avg, NFS, and DIFFBAS + NFS models.