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

• URL: http://arxiv.org/abs/2602.20549v1
• Date: Tue, 24 Feb 2026 05:06:46 GMT
• Title: Sample-efficient evidence estimation of score based priors for model selection
• Authors: Frederic Wang, Katherine L. Bouman,
• Abstract summary: We propose an estimator of the model evidence of a diffusion prior by integrating over the time-marginals of posterior sampling methods.<n>Our method leverages the large amount of intermediate samples naturally obtained during the reverse diffusion sampling process.<n>It is able to both select the correct diffusion model prior and diagnose prior misfit under different highly ill-conditioned, non-linear inverse problems.
• Score: 9.813689581505548
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 \method, 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.

Related papers

• DIVE: Inverting Conditional Diffusion Models for Discriminative Tasks [79.50756148780928]
  This paper studies the problem of leveraging pretrained diffusion models for performing discriminative tasks.<n>We extend the discriminative capability of pretrained frozen generative diffusion models from the classification task to the more complex object detection task, by "inverting" a pretrained layout-to-image diffusion model.
  arXiv  Detail & Related papers  (2025-04-24T05:13:27Z)
• A Mixture-Based Framework for Guiding Diffusion Models [19.83064246586143]
  Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems.<n>Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems.<n>This work proposes a novel mixture approximation of these intermediate distributions.
  arXiv  Detail & Related papers  (2025-02-05T16:26:06Z)
• Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements [46.03835001280626]
  Current posterior sampling-based methods take the measurement into the posterior sampling to infer the distribution of the target data.<n>We show that high-frequency information can be prematurely introduced during the early stages, which could induce larger posterior estimate errors.<n>We propose a novel diffusion posterior sampling method DPS-CM, which incorporates a Crafted Measurement (i.e., noisy measurement crafted by a reverse denoising process) to form the posterior estimate.
  arXiv  Detail & Related papers  (2024-11-15T00:06:57Z)
• Variational Diffusion Posterior Sampling with Midpoint Guidance [19.43399234028389]
  State-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior.<n>While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated.<n>We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems.
  arXiv  Detail & Related papers  (2024-10-13T18:03:53Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems [12.482127049881026]
  We propose a novel approach to solve inverse problems with a diffusion prior from an amortized variational inference perspective. Our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements.
  arXiv  Detail & Related papers  (2024-07-23T02:14:18Z)
• Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
  This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$.<n>We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
  arXiv  Detail & Related papers  (2024-05-31T16:18:46Z)
• Learning Diffusion Priors from Observations by Expectation Maximization [10.704978219090039]
  We present DiEM, a novel method for training diffusion models from incomplete and noisy observations only.<n>Unlike previous works, DiEM leads to proper diffusion models, which is crucial for downstream tasks.
  arXiv  Detail & Related papers  (2024-05-22T15:04:06Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• Projection Regret: Reducing Background Bias for Novelty Detection via Diffusion Models [72.07462371883501]
  We propose emphProjection Regret (PR), an efficient novelty detection method that mitigates the bias of non-semantic information. PR computes the perceptual distance between the test image and its diffusion-based projection to detect abnormality. Extensive experiments demonstrate that PR outperforms the prior art of generative-model-based novelty detection methods by a significant margin.
  arXiv  Detail & Related papers  (2023-12-05T09:44:47Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Decision-Making with Auto-Encoding Variational Bayes [71.44735417472043]
  We show that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing.
  arXiv  Detail & Related papers  (2020-02-17T19:23:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.