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Tweedie Moment Projected Diffusions For Inverse Problems

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arxiv 2310.06721 v3 pith:CLYHH5FM submitted 2023-10-10 stat.CO

classification stat.CO
keywords inverseproblemstweedieapproximationsbetterconditionaldiffusionearlier
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Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using Gaussian approximations to conditional densities of the reverse process via Tweedie's formula to parameterise the mean, complemented with various heuristics. To address various challenges arising from these approximations, we leverage higher order information using Tweedie's formula and obtain a statistically principled approximation. We further provide a theoretical guarantee specifically for posterior sampling which can lead to a better theoretical understanding of diffusion-based conditional sampling. Finally, we illustrate the empirical effectiveness of our approach for general linear inverse problems on toy synthetic examples as well as image restoration. We show that our method (i) removes any time-dependent step-size hyperparameters required by earlier methods, (ii) brings stability and better sample quality across multiple noise levels, (iii) is the only method that works in a stable way with variance exploding (VE) forward processes as opposed to earlier works.

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Rollout-based fine-tuning with a learned adaptive guidance scaling yields near-zero constraint violations while preserving sample fidelity in constrained diffusion models.

  5. Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach

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  6. Local MAP Sampling for Diffusion Models

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    LMAPS frames reverse-diffusion inverse-problem solving as repeated local MAP estimation, unifying existing optimization-based solvers, and achieves strong PSNR gains on tasks like motion deblurring, JPEG restoration, ...

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