InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences (2503.11043v1)

Abstract: Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restoration, leaving the performance of these algorithms in scientific inverse problems largely unexplored. To address this gap, we introduce \textsc{InverseBench}, a framework that evaluates diffusion models across five distinct scientific inverse problems. These problems present unique structural challenges that differ from existing benchmarks, arising from critical scientific applications such as optical tomography, medical imaging, black hole imaging, seismology, and fluid dynamics. With \textsc{InverseBench}, we benchmark 14 inverse problem algorithms that use plug-and-play diffusion priors against strong, domain-specific baselines, offering valuable new insights into the strengths and weaknesses of existing algorithms. To facilitate further research and development, we open-source the codebase, along with datasets and pre-trained models, at https://devzhk.github.io/InverseBench/.

An Analytical Perspective on InverseBench: Evaluating Plug-and-Play Diffusion Priors for Scientific Inverse Problems

The paper "InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences" by Zheng et al. introduces a comprehensive evaluation framework, InverseBench, which rigorously assesses the effectiveness of plug-and-play diffusion models (PnPDP) in tackling inverse problems beyond the field of natural image restoration. This paper is a pivotal step toward enhancing our understanding of these models in diverse scientific applications.

Overview of Plug-and-Play Diffusion Priors (PnPDP)

Plug-and-play diffusion priors have recently gained traction as an effective method for solving inverse problems, leveraging the power of diffusion models (DMs). These methods distinguish themselves by employing pre-trained diffusion models as flexible, decoupled priors that approximate complex high-dimensional distributions. Traditionally, PnPDP methods have been effectively applied to image restoration tasks such as inpainting and super-resolution. However, their applicability to scientific problems, where challenges such as ill-posedness and noise are more pronounced, has remained underexplored.

Benchmarking Framework and Scientific Applications

InverseBench introduces a novel benchmarking framework evaluating PnPDPs on five distinct scientific inverse problems: optical tomography, black hole imaging, medical imaging, seismology, and fluid dynamics. These tasks are representative of various scientific domains where inverse problems are prevalent, each posing unique challenges due to their domain-specific structural complexities. By encompassing such a wide spectrum, InverseBench facilitates the cross-comparison of diffusion priors with traditional methodologies, thus unveiling the nuanced capabilities and limitations of PnPDP approaches.

Methodological Diversity and Evaluation Metrics

The paper meticulously evaluates 14 different PnPDP algorithms, categorized broadly into guidance-based methods, variable splitting, variational Bayes, and Sequential Monte Carlo methods. Each algorithm's performance is assessed against domain-specific baselines, establishing a clear benchmark for comparison. A comprehensive array of metrics is employed to assess accuracy and efficiency, with particular attention paid to peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and computational complexity.

Key Insights and Implications

One of the principal findings of this paper is the robust performance of PnPDP methods when pre-trained diffusion models are available for the tasks at hand. These models consistently outperform conventional baselines, particularly in complex scenarios where prior distributions encode extensive structural details. However, the paper highlights specific scenarios where traditional methods, especially those initialized with pertinent domain knowledge, can surpass PnPDPs in precision.

Furthermore, the analysis identifies the sensitivity of PnPDP performance to the tuning of hyperparameters, especially in cases where forward modeling relies on numerical solvers governed by stability conditions, such as in PDE-constrained inverse problems. This insight is pivotal for guiding the design of more stable PnPDP algorithms.

Future Directions and Theoretical Implications

This paper not only benchmarks PnPDP performance but also sets the stage for future research directions. A critical area of exploration lies in enhancing the robustness of these models to both prior distribution mismatches and forward model uncertainties, inevitable in practical data-acquisition environments. Additionally, exploring the recovery of multi-modal solutions, a challenge evident in high-entropy problems like black hole imaging, will push the boundaries of current methodologies.

Theoretically, the findings from InverseBench provide a foundation for further enhancements in the integration of diffusion models into Bayesian frameworks, potentially leading to more expressive priors and improved sampling techniques in complex inverse problem environments.

Conclusion

Overall, InverseBench serves as a vital resource for the research community, offering a quantitative and qualitative evaluation of PnPDP methods, and guiding their development and adaptation to a broader array of scientific challenges. As diffusion models become more integrated into inverse problem-solving frameworks, the insights from this paper will be fundamental to advancing both the theoretical understanding and practical application of these powerful generative models in scientific domains.