## 4 Simulation Results
### Performance Evaluation  
As presented in Figure 5, the performance of the proposed conditional diffusion model for OFDM-based image reconstruction was demonstrated across a range of modulation schemes. In Figure 5a-c, the PSNR for the \(M_{1}\)-PSK schemes is presented for the varying SNR conditions. In low-SNR conditions, specifically ranging from 0 dB to 5 dB, the poor quality of the received images led to lower PSNR values. In this low-SNR condition, it was observed that the CDM model improved the PSNR with all \(M_{1}\)-PSK schemes, demonstrating its effectiveness in reconstructing the quality of distorted OFDM-based images through increasing the PSNR by up to 5 dB at an SNR of 0 dB and to 8 dB at an SNR of 5 dB. However, in relatively higher SNR conditions of more than 15 dB, the received images in the BPSK and QPSK scenarios exhibited higher PSNR values compared to the images reconstructed by the proposed CDM. This observation can be due to the fact that the images received with BPSK and QPSK at SNR 15 dB were almost distortion-free, and the denoising process of the CDM unintentionally degraded the image quality of the received distortion-free images. Furthermore, it was observed that the conventional diffusion model resulted in lower PSNR values than the CDM under low-SNR conditions in BPSK and QPSK, and in higher PSNR values than the CDM under high-SNR conditions. This confirmed that the conditional diffusion model, which reflects the distorted signal, is effective in recovering distorted data in low-SNR environments where signal modulation is highly distorted. On the other hand, under high-SNR conditions, the conventional diffusion model performs better because it is less distorted by modulation. For learnable and fixed variances in the conditional diffusion model, it can be noted that the CDM-LV resulted  
Figure 5: PSNR performance of the conditional diffusion model across different modulation schemes. CDM-LV: conditional diffusion model with learnable variance, CDM-FV: conditional diffusion with fixed variance, DDPM: denoising diffusion probabilistic model, Rx Data: distorted image data at the receiver. in an improvement of approximately 3 dB to 4 dB in the PSNR. This result highlights the effectiveness of learnable variance in the context of OFDM-based image reconstruction. In Figure 5d-f, the PSNR for the \(M_{2}\)-QAM schemes is presented for a varying SNR. The proposed diffusion model demonstrated consistent improvements in PSNR performance through the overall SNR range, indicating its effectiveness in reconstructing the distorted OFDM-based image under \(M_{2}\)-QAM schemes. Furthermore, it was observed that the CDM-LV approach improved the PSNR by around 4 dB at an SNR of 0 dB and 5 dB compared to the CDM-FV approach. In Figure 6, the results of the SSIM are presented for a varying SNR. It was observed that the CDM particularly enhanced the SSIM in the received data, especially in low-SNR conditions. It can also be noted that the case with the CDM-LV approach achieved an improvement higher than 0.1 at an SNR of 0 dB and 5 dB compared to that with the CDM-FV approach. This improvement implies that the proposed model can effectively preserve the structural quality of images affected by distortion, resulting in a closer alignment with the original data under low-SNR conditions. In Figure 7, the variances corresponding to the time steps are presented for the conventional diffusion process (\(\sigma_{t}\)), reverse process (\(\widetilde{\sigma}_{t}\)), and LV (\(\Sigma_{\theta}(x_{t},y,t)\)). In the CDM for OFDM-based image restoration, the initial phase of the diffusion process adheres to a fixed variance of \(\sigma_{t}\). However, with an increasing number of diffusion steps, the LV tends to adopt \(\widetilde{\sigma}_{t}\). It was confirmed that a flexible variance achieved through LV can give robustness to OFDM-based image reconstruction compared to a fixed variance.