Dual Ascent Diffusion for Inverse Problems

TL;DR

This work targets ill-posed inverse problems by leveraging pretrained diffusion priors within a dual-ascent ADMM framework (DDiff) to solve MAP problems. It replaces the standard HQS-like slotted denoising with a DDIM-based, dual-variable–augmented update scheme, enabling faster convergence and higher-quality reconstructions that maintain fidelity to the measurements even under high noise. Across five linear and three nonlinear tasks on FFHQ and ImageNet, DDiff outperforms state-of-the-art baselines (DAPS, DPS, DiffPIR) in perceptual quality (LPIPS) and residual error, while also offering robustness to noise and reduced computation due to fewer backpropagations and no extra MCMC steps. The method broadens the practical use of diffusion priors for image restoration, with potential extensions to latent diffusion models and higher-dimensional data like 3D or video.

Abstract

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior sampling approaches, however, rely on different computational approximations, leading to inaccurate or suboptimal samples. To address this issue, we introduce a new approach to solving MAP problems with diffusion model priors using a dual ascent optimization framework. Our framework achieves better image quality as measured by various metrics for image restoration problems, it is more robust to high levels of measurement noise, it is faster, and it estimates solutions that represent the observations more faithfully than the state of the art.

Figures (13)

• Figure 1: Overview of DDiff. This example illustrates the motion deblurring task. Our method alternates between three steps ($\mathbf{x}$-update, $\mathbf{z}$-update, dual update). On the right, we show the evolution of $\mathbf{x}$, $\mathbf{z}$, and $\mathbf{u}$ throughout optimization.
• Figure 2: Qualitative results. DDiff demonstrates sharper and cleaner results compared to DPS and DAPS. All tasks are run with a noise of standard deviation $\sigma=0.05$.
• Figure 3: Effect of measurement noise level. DDiff demonstrates greater robustness as noise increases. This evaluation uses 10 FFHQ validation images.
• Figure 4: Qualitative results at high measurement noise level. We use 10 randomly-chosen validation images and show the results of phase retrieval at $\sigma=0.3$, comparing our method to the state-of-the-art algorithm DAPS daps.
• Figure 5: Evaluation of time efficiency and quality of samples. The y-axis shows LPIPS value and the x-axis shows the time (in sec.) taken to generate one sample image on a GeForce RTX 2080 Ti 12GB GPU. The number after the method name (500, 2k, etc.) indicates the NFEs. This evaluation uses 100 FFHQ validation images.