Physics

Using Diffusion Models to Estimate Uncertainties in Analytic Continuation

Sagi Meir, Daniel Freedman, Barak Hirshberg

Featured August 18, 2026

AI-generated analysis — This is SciGrove's AI interpretation of the paper, not peer-reviewed content. Always refer to the original paper.

Simply

Turning fuzzy imaginary-time data into sharp real-world signals is tricky because many signals look the same. This paper uses diffusion models to generate many possible signals, showing not just one answer but all the likely ones, helping scientists understand how sure they can be about their results.

In depth

The paper tackles the ill-posed problem of analytic continuation, which involves reconstructing real-frequency spectra from imaginary-time correlation functions. Unlike traditional methods that yield single-point estimates, the authors introduce a diffusion-based generative framework that learns the full conditional probability distribution of plausible spectra. This allows for direct quantification of uncertainty and a novel assessment of the intrinsic hardness of each inversion problem.

Key Takeaways

1
The paper introduces a diffusion model for analytic continuation, moving beyond single-point estimates to model the full distribution of plausible spectra.
2
It provides a principled way to quantify uncertainty in ill-posed inverse problems by sampling from the learned conditional distribution.
3
A new metric, the Uncertainty Pseudo-Volume (UPV), is proposed to quantitatively assess the intrinsic hardness and correlated uncertainty of each inversion task.

Conceptual Flow

HIGH LEVEL

Learning All Possible Answers

Instead of guessing one answer, the method learns all the possible correct answers that fit the input data.

Fuzzy Input Data

Learn to Generate

Many Possible Answers

Knowing How Sure We Are

The method shows how much the answers can vary, helping scientists know when their results are very certain or very uncertain.

Fuzzy Input Data

Generate Many Answers

Clear Answer Range

Uncertainty Score

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