DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models (2405.16749v2)

Abstract: Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs. The code is available at https://github.com/sun-umn/DMPlug.

• The paper introduces DMPlug, a method that reparameterizes the reverse diffusion process as a deterministic function to enable unified optimization for inverse problems.
• It demonstrates significant performance improvements by achieving several dB PSNR gains over state-of-the-art methods in both linear and nonlinear scenarios.
• The method robustly handles diverse noise conditions and leverages multiple priors, making it adaptable for applications in computer vision and medical imaging.

Overview of DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models

The paper entitled "DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models" addresses the challenges of utilizing pretrained diffusion models (DMs) for inverse problems (IPs) in diverse fields such as computer vision and medical imaging. The prevailing methods typically interleave steps in the reverse diffusion process with steps enforcing measurement constraints. However, these methods often struggle with achieving manifold feasibility—ensuring that outputs appear as natural objects—and measurement feasibility—accurately fitting the measurements. Furthermore, they exhibit limitations in handling noisy IPs with unknown noise types and levels.

The authors propose DMPlug, which perceives the entire reverse process in DMs as a unified function and embeds this within a plug-in optimization framework designed to solve IPs. This approach is claimed to consistently outperform state-of-the-art methods, particularly shining in nonlinear IP scenarios and demonstrating robustness against varying noise types and levels.

Methodology and Contributions

DMPlug distinguishes itself from existing strategies by viewing the reverse diffusion process as a deterministic function represented as $R(z)$. Through reparameterizing the recovery object as $x = R(z)$, the authors formulate an optimization problem targeting the minimization of both the data-fitting loss and regularization terms, explicitly incorporating the prior from pretrained DMs. By addressing manifold and measurement feasibility within a cohesive optimization framework, DMPlug aims to converge effectively to desired solutions.

Key contributions outlined in the paper include:

• The conceptual leap of treating the reverse diffusion process as a deterministic function, avoiding the uncertainties of interleaving processes.
• Empirical evidence showing significant improvements in solving both linear and nonlinear IPs, with scenarios demonstrating PSNR improvements of several dB over previous methods.
• Adaptability to leverage multiple priors, enabling flexibility in handling IPs where different types of objects are involved.
• A method robust under unknown noise conditions, attributed to an intrinsic early-learning-followed-by-overfitting (ELTO) phenomenon, distinctly observable in DMPlug's execution.

Experimental Results

The evaluation comprehensively covers a range of IPs, including super-resolution, inpainting, nonlinear deblurring, and blind image deblurring with turbulence. Experiments were conducted over datasets such as CelebA, FFHQ, and LSUN-bedroom, involving both linear and nonlinear forward models. DMPlug is demonstrated to lead the benchmarks, especially in nonlinear tasks where it surpasses recent methods like ReSample.

Moreover, the robustness experiments included noise conditions of varying levels and types, affirming DMPlug's superior performance and reinforcing its capacity to manage uncertainty in noise properties. The authors also reflect on computational efficiencies, contrasting memory usage and execution speeds against state-of-the-art algorithms, achieving competitive metrics.

Implications and Future Directions

The proposed DMPlug method provides a promising avenue for enhancing inverse problem-solving using diffusion models, with substantial implications in areas requiring precise reconstructions from noisy measurements. The incorporation of multiple, deterministic priors inherently expands the flexibility and robustness of DMPlug, positioning it as a valuable tool across various real-world applications that demand resilience to noise and ambiguity.

The authors acknowledge some limitations, notably the empirical nature of insights into image generation vs. regression tasks. Future work could explore this discrepancy further, potentially expanding DMPlug's theoretical foundations and computational efficiency. There also remains ample scope for exploring additional problem formulations and optimizers within the plug-in framework—potentially driving further advancements in inverse problem-solving methodologies in AI.