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Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design

  • Henry Pritchard
  • Rahul Parhi
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Abstract

Plug-and-Play (PnP) methods replace proximal operators with learned denoisers, which produce state-of-the-art reconstruction quality, but sacrifice the variational interpretation and convergence guarantees of proximal methods. Learned Proximal Networks (LPNs) address this problem by designing the denoiser architecture so that it is exactly the proximal operator of a regularizer. In this work, we clarify the theoretical foundations of LPNs and extend the framework to a broader class of activation functions. We then study two practical mechanisms for controlling the learned prior: (i) averaging the LPN with the identity, a common heuristic in PnP methods, and (ii) directly scaling the implicit regularizer induced by the proximal operator. In particular, we characterize the regularizer induced by averaging and develop a convergent method for evaluating the scaled proximal operator.

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Cite

BibTeXRIS
BibTeX
@misc{pritchard2026plugandplay,
  title = {{Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design}},
  author = {Henry Pritchard and Rahul Parhi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33087},
  eprint = {2609.33087},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33087},
}
RIS
TY  - UNPB
TI  - Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design
AU  - Henry Pritchard
AU  - Rahul Parhi
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33087
UR  - https://arxiv.org/abs/2609.33087
AB  - Plug-and-Play (PnP) methods replace proximal operators with learned denoisers, which produce state-of-the-art reconstruction quality, but sacrifice the variational interpretation and convergence guarantees of proximal methods. Learned Proximal Networks (LPNs) address this problem by designing the denoiser architecture so that it is exactly the proximal operator of a regularizer. In this work, we clarify the theoretical foundations of LPNs and extend the framework to a broader class of activation functions. We then study two practical mechanisms for controlling the learned prior: (i) averaging the LPN with the identity, a common heuristic in PnP methods, and (ii) directly scaling the implicit regularizer induced by the proximal operator. In particular, we characterize the regularizer induced by averaging and develop a convergent method for evaluating the scaled proximal operator.
ER  -