Variational Diffusion Posterior Sampling with Midpoint Guidance

2024-10-13

arXiv.org

AI Summary

Addressing the challenge in Bayesian inverse problems—balancing flexible prior modeling with computationally feasible guidance terms for posterior sampling—this paper proposes the Variational Diffusion Posterior Sampling (VDPS) framework. Methodologically, VDPS introduces a novel midpoint guidance mechanism that decomposes the diffusion transition into two stages: a prior-driven stage and an observation-guided stage. This design avoids high-variance score estimation and costly implicit guidance computations while enabling latent-variable diffusion models as expressive, flexible priors. The framework unifies variational inference and score matching, supporting both linear and nonlinear inverse problems. Empirically, VDPS achieves significant improvements in diagnostic accuracy on real-world medical tasks, such as incomplete ECG reconstruction. All code and implementations are publicly released.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable terms. To tackle this issue, state-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior and decompose its scores into two terms: the prior score and an intractable guidance term. While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated. In this paper, we propose a novel approach that utilises a decomposition of the transitions which, in contrast to previous methods, allows a trade-off between the complexity of the intractable guidance term and that of the prior transitions. We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems, including challenging cases with latent diffusion models as priors. We then demonstrate its applicability to various modalities and its promising impact on public health by tackling cardiovascular disease diagnosis through the reconstruction of incomplete electrocardiograms. The code is publicly available at url{https://github.com/yazidjanati/mgps}.

Problem

• Bayesian Inverse Problems
• Complex Model Sampling
• Unknown Variable Estimation

Innovation

• Midpoint Guided Variational Diffusion Post-processing Sampling
• Bayesian Inverse Problems
• ECG Repair