Diffusion Posterior Sampling for Super-Resolution under Gaussian Measurement Noise

Abstract: This report studies diffusion posterior sampling (DPS) for single-image super-resolution (SISR) under a known degradation model. We implement a likelihood-guided sampling procedure that combines an unconditional diffusion prior with gradient-based conditioning to enforce measurement consistency for $4\times$ super-resolution with additive Gaussian noise. We evaluate posterior sampling (PS) conditioning across guidance scales and noise levels, using PSNR and SSIM as fidelity metrics and a combined selection score $(\mathrm{PSNR}/40)+\mathrm{SSIM}$. Our ablation shows that moderate guidance improves reconstruction quality, with the best configuration achieved at PS scale $0.95$ and noise standard deviation $σ=0.01$ (score $1.45231$). Qualitative results confirm that the selected PS setting restores sharper edges and more coherent facial details compared to the downsampled inputs, while alternative conditioning strategies (e.g., MCG and PS-annealed) exhibit different texture fidelity trade-offs. These findings highlight the importance of balancing diffusion priors and measurement-gradient strength to obtain stable, high-quality reconstructions without retraining the diffusion model for each operator.