Bayesian Conditioned Diffusion Models for Inverse Problems
<|reference_start|>Bayesian Conditioned Diffusion Models for Inverse Problems: Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later post-conditioned for reconstruction, an approach that typically suffers from suboptimal task performance. While task-specific conditional models have also been proposed, current methods heuristically inject measured data as a naive input channel that elicits sampling inaccuracies. Here, we address the optimal conditioning of diffusion models for solving challenging inverse problems that arise during image reconstruction. Specifically, we propose a novel Bayesian conditioning technique for diffusion models, BCDM, based on score-functions associated with the conditional distribution of desired images given measured data. We rigorously derive the theory to express and train the conditional score-function. Finally, we show state-of-the-art performance in image dealiasing, deblurring, super-resolution, and inpainting with the proposed technique.<|reference_end|>
@article{güngör2024bayesian,
    title={Bayesian Conditioned Diffusion Models for Inverse Problems},
    author={Alper G"ung"or, Bahri Batuhan Bilecen, Tolga c{C}ukur},
    journal={arXiv preprint arXiv:2406.09768},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.09768},
    primaryClass={cs.CV cs.AI cs.LG}
}