Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver

• URL: http://arxiv.org/abs/2508.02964v1
• Date: Tue, 05 Aug 2025 00:01:41 GMT
• Title: Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver
• Authors: Jonathan Patsenker, Henry Li, Myeongseob Ko, Ruoxi Jia, Yuval Kluger,
• Abstract summary: We propose to estimate the conditional posterior mean $mathbbE [mathbfx_t, mathbfy]$.<n>The resulting prediction can be integrated into any standard sampler, resulting in a fast and memory-efficient inverse solver.
• Score: 20.959606647379356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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