Inverse problems with diffusion models: MAP estimation via mode-seeking loss
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| Format: | Preprint |
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2025
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| author | Gutha, Sai Bharath Chandra Vinuesa, Ricardo Azizpour, Hossein |
| author_facet | Gutha, Sai Bharath Chandra Vinuesa, Ricardo Azizpour, Hossein |
| contents | A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing posterior sampling and MAP estimation methods often rely on modeling approximations and can also be computationally demanding. In this work, we propose a new MAP estimation strategy for solving inverse problems with a pre-trained unconditional diffusion model. Specifically, we introduce the variational mode-seeking loss (VML) and show that its minimization at each reverse diffusion step guides the generated sample towards the MAP estimate (modes in practice). VML arises from a novel perspective of minimizing the Kullback-Leibler (KL) divergence between the diffusion posterior $p(\mathbf{x}_0|\mathbf{x}_t)$ and the measurement posterior $p(\mathbf{x}_0|\mathbf{y})$, where $\mathbf{y}$ denotes the measurement. Importantly, for linear inverse problems, VML can be analytically derived without any modeling approximations. Based on further theoretical insights, we propose VML-MAP, an empirically effective algorithm for solving inverse problems via VML minimization, and validate its efficacy in both performance and computational time through extensive experiments on diverse image-restoration tasks across multiple datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse problems with diffusion models: MAP estimation via mode-seeking loss Gutha, Sai Bharath Chandra Vinuesa, Ricardo Azizpour, Hossein Machine Learning Computer Vision and Pattern Recognition A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing posterior sampling and MAP estimation methods often rely on modeling approximations and can also be computationally demanding. In this work, we propose a new MAP estimation strategy for solving inverse problems with a pre-trained unconditional diffusion model. Specifically, we introduce the variational mode-seeking loss (VML) and show that its minimization at each reverse diffusion step guides the generated sample towards the MAP estimate (modes in practice). VML arises from a novel perspective of minimizing the Kullback-Leibler (KL) divergence between the diffusion posterior $p(\mathbf{x}_0|\mathbf{x}_t)$ and the measurement posterior $p(\mathbf{x}_0|\mathbf{y})$, where $\mathbf{y}$ denotes the measurement. Importantly, for linear inverse problems, VML can be analytically derived without any modeling approximations. Based on further theoretical insights, we propose VML-MAP, an empirically effective algorithm for solving inverse problems via VML minimization, and validate its efficacy in both performance and computational time through extensive experiments on diverse image-restoration tasks across multiple datasets. |
| title | Inverse problems with diffusion models: MAP estimation via mode-seeking loss |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2512.10524 |