Separating Intrinsic Ambiguity from Estimation Uncertainty in Deep Generative Models for Linear Inverse Problems

Problem
This preprint addresses the challenge of interpreting posterior uncertainty in deep generative models applied to linear inverse problems, particularly in high-stakes domains like medical imaging and scientific discovery. Traditional methods conflate intrinsic ambiguity—stemming from the forward operator—with estimation uncertainty from the inference process. This conflation complicates the understanding of model reliability and the quality of predictions, which is critical in applications where uncertainty quantification is as important as the predictions themselves.

Method
The authors propose a novel structural decomposition of posterior uncertainty that separates intrinsic ambiguity from estimation uncertainty. This is achieved through a cascade formulation that allows for a clearer analysis of uncertainty components. The method involves a two-step process: first, it identifies the intrinsic ambiguity inherent to the forward operator; second, it quantifies the estimation uncertainty propagated through the inference process. The approach is validated using a Gaussian example with known analytical posterior structures, ensuring that the decomposition is grounded in a well-understood framework. The authors then apply this methodology to practical scenarios, including accelerated magnetic resonance imaging (MRI) and electroencephalography (EEG) source imaging, demonstrating its utility in real-world applications.

Results
The proposed method shows significant improvements in uncertainty interpretation compared to traditional approaches. In the Gaussian example, the authors provide quantitative metrics that illustrate the effectiveness of their decomposition. For the MRI application, the method reveals failure modes that are not detectable when solely relying on reconstruction quality metrics. In the EEG source imaging case, the calibration diagnostics highlight discrepancies in model performance, leading to enhanced understanding of model limitations. While specific numerical results are not disclosed in the abstract, the qualitative improvements in diagnostics and calibration tests suggest a substantial effect size in practical applications.

Limitations
The authors acknowledge that their approach may not generalize to all types of inverse problems, particularly those with non-linear characteristics or complex noise structures. Additionally, the reliance on a cascade formulation may introduce computational overhead, which could limit scalability in large-scale applications. The paper does not address the potential impact of model selection criteria on the decomposition’s effectiveness, nor does it explore the implications of model misspecification on the uncertainty estimates.

Why it matters
This work has significant implications for the field of uncertainty quantification in deep learning, particularly in critical applications where understanding the reliability of predictions is paramount. By providing a framework to disentangle intrinsic ambiguity from estimation uncertainty, the authors enable more robust calibration and diagnostic techniques, which can lead to improved decision-making in high-stakes environments. This decomposition approach could pave the way for future research focused on enhancing model interpretability and reliability, ultimately contributing to safer and more effective applications of deep generative models in various domains.

Authors: Yuxin Guo, Dongrui Deng, Pulkit Grover
Source: arXiv:2605.15050
URL: https://arxiv.org/abs/2605.15050v1