MAP Estimation with Denoisers: Convergence Rates and Guarantees

• URL: http://arxiv.org/abs/2507.15397v1
• Date: Mon, 21 Jul 2025 08:59:33 GMT
• Title: MAP Estimation with Denoisers: Convergence Rates and Guarantees
• Authors: Scott Pesme, Giacomo Meanti, Michael Arbel, Julien Mairal,
• Abstract summary: We show that a simple algorithm converges to the proximal operator under a log-concavity assumption on the prior $p$.<n>We show that this algorithm can be interpreted as a gradient descent on smoothed proximal objectives.
• Score: 37.88502562012743
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving Maximum a Posteriori (MAP) optimisation problems, where the proximal operator of the negative log-prior plays a central role. In practice, this operator is intractable, and practitioners plug in a pretrained denoiser as a surrogate-despite the lack of general theoretical justification for this substitution. In this work, we show that a simple algorithm, closely related to several used in practice, provably converges to the proximal operator under a log-concavity assumption on the prior $p$. We show that this algorithm can be interpreted as a gradient descent on smoothed proximal objectives. Our analysis thus provides a theoretical foundation for a class of empirically successful but previously heuristic methods.

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