# Sample-efficient evidence estimation of score based priors for model selection

arXiv: https://arxiv.org/abs/2602.20549 · HTML: https://mlsanity.com/paper/2602.20549/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [Score-Based Diffusion meets Annealed Importance Sampling](https://mlsanity.com/paper/2208.07698/) (2022)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [Split-and-augmented Gibbs sampler - Application to large-scale inference problems](https://mlsanity.com/paper/1804.05809/) (2018)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [The Superposition of Diffusion Models Using the Ito Density Estimator](https://mlsanity.com/paper/2412.17762/) (2024)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Proximal nested sampling for high-dimensional Bayesian model selection](https://mlsanity.com/paper/2106.03646/) (2021)
- [Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond](https://mlsanity.com/paper/2502.04575/) (2025)
- [Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator](https://mlsanity.com/paper/2111.12720/) (2021)
- [FLARE up your data: Diffusion-based Augmentation Method in Astronomical Imaging](https://mlsanity.com/paper/2405.13267/) (2024)
- [Event-horizon-scale Imaging of M87* under Different Assumptions via Deep Generative Image Priors](https://mlsanity.com/paper/2406.02785/) (2024)
- [Learned harmonic mean estimation of the marginal likelihood with normalizing flows](https://mlsanity.com/paper/2307.00048/) (2023)

## Built on by (most cited first, 3 of 3)

- [Optimizing Diffusion Priors in Image Reconstruction from a Single Observation](https://mlsanity.com/paper/2604.21066/) (2026)
- [Lightweight 3D Feature Pretraining by Bayesian Inversion of 2D Foundation Models](https://mlsanity.com/paper/2606.21292/) (2026)
- [Evidence-Aligned Local Composition of Discrete Experts for Sequence Restoration](https://mlsanity.com/paper/2609.05801/) (2026)

## Abstract (arXiv)

The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements y to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating the model evidence p(y mid M) under different models M that specify the prior and then selecting the one with the highest value. Diffusion models are the state-of-the-art approach to solving inverse problems with a data-driven prior; however, directly computing the model evidence with respect to a diffusion prior is intractable. Furthermore, most existing model evidence estimators require either many pointwise evaluations of the unnormalized prior density or an accurate clean prior score. We propose DiME, an estimator of the model evidence of a diffusion prior by integrating over the time-marginals of posterior sampling methods. Our method leverages the large amount of intermediate samples naturally obtained during the reverse diffusion sampling process to obtain an accurate estimation of the model evidence using only a handful of posterior samples (e.g., 20). We also demonstrate how to implement our estimator in tandem with recent diffusion posterior sampling methods. Empirically, our estimator matches the model evidence when it can be computed analytically, and it is able to both select the correct diffusion model prior and diagnose prior misfit under different highly ill-conditioned, non-linear inverse problems, including a real-world black hole imaging problem.