{"ID":2886039,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.02964","arxiv_id":"2508.02964","title":"Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver","abstract":"Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula, which relates the diffusion variate $\\mathbf{x}_t$ to the posterior mean $\\mathbb{E} [\\mathbf{x}_0 | \\mathbf{x}_t]$, in order to guide the diffusion trajectory with an estimate of the final denoised sample $\\mathbf{x}_0$. However, this does not consider information from the measurement $\\mathbf{y}$, which must then be integrated downstream. In this work, we propose to estimate the conditional posterior mean $\\mathbb{E} [\\mathbf{x}_0 | \\mathbf{x}_t, \\mathbf{y}]$, which can be formulated as the solution to a lightweight, single-parameter maximum likelihood estimation problem. The resulting prediction can be integrated into any standard sampler, resulting in a fast and memory-efficient inverse solver. Our optimizer is amenable to a noise-aware likelihood-based stopping criteria that is robust to measurement noise in $\\mathbf{y}$. We demonstrate comparable or improved performance against a wide selection of contemporary inverse solvers across multiple datasets and tasks.","short_abstract":"Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula, which relates the diffusion variate $\\mathbf{x}_t$ to the posterior mean $\\math...","url_abs":"https://arxiv.org/abs/2508.02964","url_pdf":"https://arxiv.org/pdf/2508.02964v3","authors":"[\"Jonathan Patsenker\",\"Henry Li\",\"Myeongseob Ko\",\"Ruoxi Jia\",\"Yuval Kluger\"]","published":"2025-08-05T00:01:41Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.CO\"]","methods":"[\"Diffusion Model\"]","has_code":false}