PnP-Flow: Plug-and-Play Image Restoration with Flow Matching (2410.02423v2)

Abstract: In this paper, we introduce Plug-and-Play (PnP) Flow Matching, an algorithm for solving imaging inverse problems. PnP methods leverage the strength of pre-trained denoisers, often deep neural networks, by integrating them in optimization schemes. While they achieve state-of-the-art performance on various inverse problems in imaging, PnP approaches face inherent limitations on more generative tasks like inpainting. On the other hand, generative models such as Flow Matching pushed the boundary in image sampling yet lack a clear method for efficient use in image restoration. We propose to combine the PnP framework with Flow Matching (FM) by defining a time-dependent denoiser using a pre-trained FM model. Our algorithm alternates between gradient descent steps on the data-fidelity term, reprojections onto the learned FM path, and denoising. Notably, our method is computationally efficient and memory-friendly, as it avoids backpropagation through ODEs and trace computations. We evaluate its performance on denoising, super-resolution, deblurring, and inpainting tasks, demonstrating superior results compared to existing PnP algorithms and Flow Matching based state-of-the-art methods.

• The paper presents a novel Plug-and-Play flow matching method that integrates a time-dependent denoiser for robust image restoration.
• It employs a forward-backward splitting framework, combining gradient descent with learned flow paths to enhance data fidelity.
• Experimental results across multiple datasets show improved PSNR and SSIM, consistently surpassing state-of-the-art performance.

Overview of "PnP-F LOW: Plug-And-Play Image Restoration with Flow Matching"

The paper presents an innovative approach to addressing inverse imaging problems using a proposed algorithm called Plug-and-Play (PnP) Flow Matching. This method integrates pre-trained denoisers with optimization schemes to achieve robust image restoration outcomes. Specifically, the PnP Flow Matching algorithm relies on a generative model known as Flow Matching, which focuses on learning a velocity field that maps a latent distribution to the data distribution. This velocity field operates as a time-dependent denoiser within the modified optimization framework.

Building on foundational concepts from Plug-and-Play methodologies and recent advances in generative modeling, the authors devised an algorithm that alternates between gradient descent steps focused on data fidelity, reprojections from learned flow paths, and denoising actions. This makes the proposed PnP Flow Matching computationally efficient and memory conservative, by bypassing challenges related to backpropagation through ordinary differential equations (ODEs) and trace computation typically inherent in similar methods.

Methodological Contributions

Several key contributions emerge from this approach:

• Time-Dependent Denoiser: The design of a novel denoiser that leverages pre-trained velocity fields derived from Flow Matching, which allows the computational system to dynamically adjust denoising operations over time.
• Forward-Backward Splitting Framework: The algorithm employs a forward-backward splitting model, optimized with gradient steps and linear interpolation ensuring that the denoising step is both time-dependent and effective in maintaining fidelity to flow paths learned via Flow Matching.
• Performance and Efficiency: The algorithm demonstrates significant efficiency improvements in computational time and memory usage compared to existing approaches. This is particularly advantageous when extending the methodology to larger images and more complex tasks.
• Evaluation Metrics: Across various restoration tasks like denoising, deblurring, inpainting, and super-resolution, the PnP Flow algorithm consistently surpasses the performance of prevailing state-of-the-art approaches using PSNR and SSIM as evaluation metrics.

Experimental Framework

The evaluation of the method was conducted on multiple datasets (CelebA and AFHQ-Cat) with tasks covering a broad spectrum of image restoration challenges. The results showed consistently improved image quality and stability across diverse tasks, aligning with the state-of-the-art or achieving first-rank performance. An important aspect of the experimentation was the method's capability to operate under varying conditions such as different noise levels and types of image degradation, showcasing its robust adaptability.

Implications and Future Directions

From a practical standpoint, the implications of utilizing flow matching as a denoising operator in a PnP framework are profound. This strategy enables the flexible use of different latent distributions beyond Gaussian priors, thus potentially improving the model's applicability across various domains, including medical imaging and scientific data analysis where specific noise models or data distributions are present.

Theoretically, the paper extends the understanding of how flow-based generative models can synergize with plug-and-play frameworks, potentially inspiring novel intersections between inversion methodologies and data-adaptive priors. Looking forward, research could explore the application of PnP Flow Matching in other inverse problems beyond imaging, such as those incorporating categorical distributions using Dirichlet priors. There is also potential for advancing the model's adaptability to other noise types, fostering its eventual deployment in more specialized domains.

In conclusion, the PnP Flow Matching method embodies a notable step forward in the landscape of image restoration by innovatively combining generative and optimization paradigms, paving the way for more computationally tractable and versatile image processing solutions.