Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Diffusion Posterior Sampling for Super-Resolution under Gaussian Measurement Noise

Abu Hanif Muhammad Syarubany

TL;DR

This work addresses 4× single-image super-resolution under Gaussian measurement noise by framing SISR as an inverse problem with $y = A(x_0) + n$ and solving it via diffusion posterior sampling (DPS). A pretrained unconditional diffusion prior is augmented with a likelihood-guided update that enforces data fidelity during reverse diffusion, enabling plug-and-play restoration without retraining for each operator. An ablation over guidance scale and noise level identifies a best configuration at a PS guidance scale of $0.95$ with $\sigma = 0.01$, achieving a combined score of $1.45231$ (PSNR/SSIM), and qualitative results show sharper edges and more coherent facial details than the degraded input. The findings demonstrate the importance of balancing diffusion priors and measurement-gradient strength to achieve stable, high-quality reconstructions in a practical, operator-agnostic framework suitable for diverse inverse problems.

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.

Diffusion Posterior Sampling for Super-Resolution under Gaussian Measurement Noise

TL;DR

This work addresses 4× single-image super-resolution under Gaussian measurement noise by framing SISR as an inverse problem with and solving it via diffusion posterior sampling (DPS). A pretrained unconditional diffusion prior is augmented with a likelihood-guided update that enforces data fidelity during reverse diffusion, enabling plug-and-play restoration without retraining for each operator. An ablation over guidance scale and noise level identifies a best configuration at a PS guidance scale of with , achieving a combined score of (PSNR/SSIM), and qualitative results show sharper edges and more coherent facial details than the degraded input. The findings demonstrate the importance of balancing diffusion priors and measurement-gradient strength to achieve stable, high-quality reconstructions in a practical, operator-agnostic framework suitable for diverse inverse problems.

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 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 . Our ablation shows that moderate guidance improves reconstruction quality, with the best configuration achieved at PS scale and noise standard deviation (score ). 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.
Paper Structure (16 sections, 7 equations, 3 figures, 1 table, 2 algorithms)

This paper contains 16 sections, 7 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Inverse Problem Formulation (Super-Resolution)
  5. Diffusion Prior and Unconditional Reverse Sampling
  6. Conditional Sampling via Denoising Posterior Sampling (DPS)
  7. Backpropagation through the pipeline.
  8. Conditioning Modules Used in Our Implementation
  9. Practical Notes (Implementation Mapping)
  10. Experiments and Results
  11. Experimental Setup
  12. Quantitative Results
  13. Configuration Selection
  14. Qualitative Results
  15. Discussion
  16. ...and 1 more sections

Figures (3)

  • Figure 1: DPS guidance pipeline at timestep $t$. The denoiser predicts $\hat{\epsilon}_\theta(x_t,t)$ and forms $\hat{x}_0(x_t,t)$ via Tweedie’s formula. The forward operator produces $\mathcal{A}(\hat{x}_0)$, which is compared to the measurement $y$ to compute a residual. Gradients are backpropagated through $\mathcal{A}(\cdot)$ and $\hat{x}_0(x_t,t)$ to update the sample for measurement-consistent reverse diffusion.
  • Figure 2: Qualitative comparison for super-resolution using the selected PS configuration (scale $=0.9$, $\sigma=0.01$). Top: downsampled measurement (input). Bottom: reconstructed output.
  • Figure 3: Qualitative comparison across samplers/conditioning methods. First row: DDIM sampler. Remaining rows: DDPM sampler with different conditioning methods (MCG, PS annealed, Vanilla PS).