Think Twice Before You Act: Improving Inverse Problem Solving With MCMC
Yaxuan Zhu, Zehao Dou, Haoxin Zheng, Yasi Zhang, Ying Nian Wu, Ruiqi, Gao
TL;DR
This paper introduces DPMC, an annealed MCMC-based inference method that enhances diffusion model-based inverse problem solving by reducing approximation errors, outperforming previous methods like DPS across multiple tasks.
Contribution
The paper proposes DPMC, a novel annealed MCMC algorithm that improves inverse problem solving with diffusion models by reducing accumulated errors during sampling.
Findings
DPMC outperforms DPS with fewer evaluations in various inverse tasks.
DPMC is competitive with existing approaches in inverse problem solving.
The method effectively reduces approximation errors in high noise scenarios.
Abstract
Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure using Tweedie's formula. Despite the merits of being versatile in solving various inverse problems without re-training, the performance of DPS is hindered by the fact that this posterior approximation can be inaccurate especially for high noise levels. Therefore, we propose \textbf{D}iffusion \textbf{P}osterior \textbf{MC}MC (\textbf{DPMC}), a novel inference algorithm based on Annealed MCMC to solve inverse problems with pretrained diffusion models. We define a series of intermediate distributions inspired by the approximated conditional distributions used by DPS. Through annealed MCMC sampling, we encourage the samples to follow each intermediate…
Peer Reviews
Decision·ICLR 2025 Conference Withdrawn Submission
1) The empirical results are quite strong. The authors demonstrate that their method outperforms natural baselines across different inverse problems such as mask inpainting, box inpainting, super-resolution, deblurring, and phase retrieval. 2) The algorithmic modification is simple, which might allow for wide adoption from the community. 3) The research direction of developing algorithms for solving inverse problems with diffusion models is relevant and interesting.
1) I believe that the presentation of the paper could be improved. There are several examples. In Line 43, I believe that measure should be changed to measurement. In Lines 46-47, I believe that the authors want to say that the posterior is intractable (it is always defined, but it is intractable to sample from it or write down an explicit formula for its density). I also believe that it is a little confusing to what former and later refer to in lines 158-159. The theoretical result is not clear
1. The theoretical bound presented in the appendix is insightful. 2. The paper is well-structured and easy to follow (altough there are some problems with writing as I explained in the weakness part). 3. The experimental results demonstrate the superiority of the proposed method over state-of-the-art alternatives, both quantitatively and qualitatively. 4. The experiments are thorough and consider relevant datasets and settings.
1. **Marginal Contribution**: The contribution of the paper appears limited, as it primarily applies the established MCMC algorithm within diffusion models for solving inverse problems. Specifically, the novelty seems to lie in the use of Equation (10) atop standard diffusion models, where Equation (10) serves as the MCMC update step. 2. **Method Clarity**: The authors should dedicate more space to clearly explaining their method in Section 3, especially detailing the deployment of MCMC in pos
1. This paper aims to reduce the bias in diffusion posterior sampling by incorporating MCMC sampling into the intermediate steps of the reverse diffusion process. 2. The experimental results are promising across a range of inverse tasks, including super-resolution (4x), random inpainting, motion deblurring, Gaussian deblurring, and box inpainting.
1. In the Line 6 of Algorithm 1, the update follows Eq 10. The second term in Eq 10 requires $\nabla \log p_t(x_t)$ and the gradient of the measurement error. How is the score function $\nabla \log p_t(x_t)$ computed using the pre-trained neural network? Since the NN expects the state and time as inputs, and time changes after every update, how is the time step (or equivalently the noise level) chosen while computing the score? 2. The proposed DPMC sampler is a stochastic equivalent of RB-Modul
**Originality**: While the proposed idea of using annealed MCMC has been utilized for unconditional diffusion sampling in several prior works [Song et al.], its application to solving inverse problems combined with existing posterior approximation methods is novel. **Quality and Clarity**: The paper is written clearly, and the choice of baselines is adequate. The empirical results in Tables 1 and 2 are comprehensive regarding the selection of datasets and inverse problems. The ablation studies
**Requested Changes/Questions** 1. **On the choice of the intermediate distribution in Eq. 9**: The authors use the posterior approximation from DPS to define the intermediate distributions as stated in Eq. 9. In principle, the approximation from Pi-GDM can also be used to formulate the same. What is the rationale behind sticking with the approximation in DPS since Pi-GDM can perform better with fewer NFE? It would be great if the authors could clarify this choice in the main text. 2. **On the
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Taxonomy
TopicsComplex Systems and Decision Making · Problem and Project Based Learning · Teaching and Learning Programming
MethodsDiffusion