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.
| Subjects: | Machine Learning (cs.LG); Computation (stat.CO) |
| Cite as: | arXiv:2508.02964 [cs.LG] |
| (or arXiv:2508.02964v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2508.02964 arXiv-issued DOI via DataCite |
From: Jonathan Patsenker [view email]
[v1]
Tue, 5 Aug 2025 00:01:41 UTC (44,409 KB)
[v2]
Thu, 2 Oct 2025 21:56:22 UTC (44,413 KB)
[v3]
Tue, 28 Apr 2026 04:04:44 UTC (8,372 KB)
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