Mode-Seeking for Inverse Problems with Diffusion Models
- URL: http://arxiv.org/abs/2512.10524v1
- Date: Thu, 11 Dec 2025 10:51:34 GMT
- Title: Mode-Seeking for Inverse Problems with Diffusion Models
- Authors: Sai Bharath Chandra Gutha, Ricardo Vinuesa, Hossein Azizpour,
- Abstract summary: 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.<n>In this work, we propose the variational mode-seeking loss (VML), which guides the generated sample towards the MAP estimate.<n>VML arises from a novel perspective of minimizing the Kullback-Leibler (KL) divergence between the diffusion posterior $p(mathbfx_0|mathbfx_t)$ and the measurement posterior $p(mathbfx
- Score: 10.660734390023912
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 be computationally demanding. In this work, we propose the variational mode-seeking loss (VML), which, when minimized during each reverse diffusion step, guides the generated sample towards the MAP estimate. 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 and need not be approximated. Based on further theoretical insights, we propose VML-MAP, an empirically effective algorithm for solving inverse problems, and validate its efficacy over existing methods in both performance and computational time, through extensive experiments on diverse image-restoration tasks across multiple datasets.
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