arXiv:2606.17048v1 Announce Type: new Abstract: 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 f
This research builds on recent advances in diffusion and flow-based models, which are becoming increasingly central to AI research and applications, indicating a natural progression in their theoretical foundations.
Improving the theoretical understanding and practical application of diffusion models for inverse problems can lead to more robust and accurate AI systems in imaging, scientific computing, and generative AI.
The ability to derive exact posterior scores for linear inverse problems offers a more principled approach to using pretrained denoisers, potentially leading to more efficient and higher-quality solutions compared to current approximation methods.
- · AI researchers
- · Image processing sector
- · Scientific computing
- · Deep learning practitioners
- · Methods relying solely on approximate priors
- · Less robust restoration algorithms
More accurate and versatile generative models for inverse problems will emerge.
This could accelerate breakthroughs in fields like medical imaging, computational photography, and materials science.
The enhanced capability of AI to 'see' and reconstruct information from noisy or incomplete data might lead to new scientific discoveries and industrial applications currently deemed impossible.
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Read at arXiv cs.LG