{"ID":2866770,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.20511","arxiv_id":"2509.20511","title":"A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm","abstract":"Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but rigorous recovery guarantees remain limited. In this work, we develop a theoretical framework for analyzing deterministic diffusion-based algorithms for inverse problems, focusing on a deterministic version of the algorithm proposed by Kadkhodaie \\\u0026 Simoncelli \\cite{kadkhodaie2021stochastic}. First, we show that when the underlying data distribution concentrates on a low-dimensional model set, the associated noise-convolved scores can be interpreted as time-varying projections onto such a set. This leads to interpreting previous algorithms using diffusion priors for inverse problems as generalized projected gradient descent methods with varying projections. When the sensing matrix satisfies a restricted isometry property over the model set, we can derive quantitative convergence rates that depend explicitly on the noise schedule. We apply our framework to two instructive data distributions: uniform distributions over low-dimensional compact, convex sets and low-rank Gaussian mixture models. In the latter setting, we can establish global convergence guarantees despite the nonconvexity of the underlying model set.","short_abstract":"Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but rigorous recovery guarantees remain limited. In this work, we develop a theoretic...","url_abs":"https://arxiv.org/abs/2509.20511","url_pdf":"https://arxiv.org/pdf/2509.20511v1","authors":"[\"Oscar Leong\",\"Yann Traonmilin\"]","published":"2025-09-24T19:35:23Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}