Bayesian Conditioned Diffusion Models for Inverse Problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911918097170432 |
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| author | Güngör, Alper Bilecen, Bahri Batuhan Çukur, Tolga |
| author_facet | Güngör, Alper Bilecen, Bahri Batuhan Çukur, Tolga |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian Conditioned Diffusion Models for Inverse Problems Güngör, Alper Bilecen, Bahri Batuhan Çukur, Tolga Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning 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. |
| title | Bayesian Conditioned Diffusion Models for Inverse Problems |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2406.09768 |