Exact Posterior Score Estimation for Solving Linear Inverse Problems
Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption. To use this prior to solve a linear inverse problem, one needs to sample from the posterior, but the score that the prior provides is the unconditional score, not the posterior score. Existing methods either steer a fixed pretrained denoiser with approximate measurement-matching corrections, or train a conditional restoration model that abandons the denoising structure of the prior. We derive the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, and show that posterior sampling reduces to a denoising problem at an op...
| Authors | Abbas Mammadov, Ozgur Kara, Kaan Oktay et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 June 2026 |
| Last updated at source | 15 June 2026 |
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