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Plug-and-Play Priors as a Score-Based Method

Chicago Y. Park, Yuyang Hu, Michael T. McCann, Cristina Garcia-Cardona, Brendt Wohlberg, Ulugbek S. Kamilov

TL;DR

This work reframes Plug-and-Play priors as a score-based method, enabling pre-trained score-based diffusion models to serve as priors inside classical PnP algorithms without retraining. By deriving a general Tweedie-based template, any SBM score can be converted into a PnP denoiser $\mathsf{D}_{\sigma}(\mathbf{x})$ and integrated with PnP-ADMM or RED, including explicit mappings for VE and VP diffusion models and a parameter_matching mechanism to align noise levels. The authors demonstrate improved reconstruction quality over traditional CNN-based priors on motion deblurring tasks and show that DiffPIR using the same SBM prior offers competitive posterior sampling performance, facilitating fair comparisons between PnP and diffusion-based approaches. This approach broadens the practical utility of SBMs in inverse problems, leveraging powerful, openly available priors without retraining while preserving convergence guarantees. Code for the method is publicly available at the provided repository.

Abstract

Plug-and-play (PnP) methods are extensively used for solving imaging inverse problems by integrating physical measurement models with pre-trained deep denoisers as priors. Score-based diffusion models (SBMs) have recently emerged as a powerful framework for image generation by training deep denoisers to represent the score of the image prior. While both PnP and SBMs use deep denoisers, the score-based nature of PnP is unexplored in the literature due to its distinct origins rooted in proximal optimization. This letter introduces a novel view of PnP as a score-based method, a perspective that enables the re-use of powerful SBMs within classical PnP algorithms without retraining. We present a set of mathematical relationships for adapting popular SBMs as priors within PnP. We show that this approach enables a direct comparison between PnP and SBM-based reconstruction methods using the same neural network as the prior. Code is available at https://github.com/wustl-cig/score_pnp.

Plug-and-Play Priors as a Score-Based Method

TL;DR

This work reframes Plug-and-Play priors as a score-based method, enabling pre-trained score-based diffusion models to serve as priors inside classical PnP algorithms without retraining. By deriving a general Tweedie-based template, any SBM score can be converted into a PnP denoiser and integrated with PnP-ADMM or RED, including explicit mappings for VE and VP diffusion models and a parameter_matching mechanism to align noise levels. The authors demonstrate improved reconstruction quality over traditional CNN-based priors on motion deblurring tasks and show that DiffPIR using the same SBM prior offers competitive posterior sampling performance, facilitating fair comparisons between PnP and diffusion-based approaches. This approach broadens the practical utility of SBMs in inverse problems, leveraging powerful, openly available priors without retraining while preserving convergence guarantees. Code for the method is publicly available at the provided repository.

Abstract

Plug-and-play (PnP) methods are extensively used for solving imaging inverse problems by integrating physical measurement models with pre-trained deep denoisers as priors. Score-based diffusion models (SBMs) have recently emerged as a powerful framework for image generation by training deep denoisers to represent the score of the image prior. While both PnP and SBMs use deep denoisers, the score-based nature of PnP is unexplored in the literature due to its distinct origins rooted in proximal optimization. This letter introduces a novel view of PnP as a score-based method, a perspective that enables the re-use of powerful SBMs within classical PnP algorithms without retraining. We present a set of mathematical relationships for adapting popular SBMs as priors within PnP. We show that this approach enables a direct comparison between PnP and SBM-based reconstruction methods using the same neural network as the prior. Code is available at https://github.com/wustl-cig/score_pnp.

Paper Structure

This paper contains 6 sections, 13 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Score Adaptation for PnP
  4. Numerical evaluation
  5. Conclusion
  6. Acknowledgment

Figures (2)

  • Figure 1: Visual comparison of three classical PnP methods for motion deblurring on color images. DPIR, PnP-ADMM, and RED are compared with CNN-based and SBM-based priors ho_NEURIPS2020_ddpm. The figure also includes the results of DiffPIR using the same SBM as the prior. Note how our framework enables the direct comparison of DiffPIR with three classical PnP methods using exactly the same neural network as the prior.
  • Figure : PnP-ADMM with score-based denoising