Optimizing Diffusion Priors with a Single Observation

2026-04-24 · Source: cs.CV updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Image Processing & Computer Vision · Depth: Expert, extended

Summary

Caltech researchers have developed a novel method for optimizing diffusion priors in image reconstruction, particularly from a single observation. This approach addresses the limitations of diffusion models trained on restricted or simulated datasets, which often inherit biases or errors. Instead of requiring numerous observations for fine-tuning, the proposed method combines existing diffusion priors into a "product-of-experts" prior and identifies optimal exponent weights by maximizing Bayesian evidence. The technique was validated on real-world inverse problems, including black hole imaging using Event Horizon Telescope (EHT) data and image deblurring with text-conditioned Stable Diffusion priors. Experiments demonstrated that the evidence is frequently maximized by priors that extend beyond those trained on a single dataset, leading to more flexible and trustworthy posterior image distributions. The method introduces two strategies for exponent selection: an evidence scalar field estimation for two priors and a generalized expectation-maximization (EM) method for multiple priors.

Key takeaway

For Computer Vision Engineers working on under-constrained inverse imaging problems with limited data, this method offers a principled way to adapt diffusion priors. You can improve reconstruction trustworthiness and reduce bias by combining and tempering existing diffusion models, even with only a single observation. Consider applying the generalized EM method to optimize prior exponents, especially when dealing with multiple candidate priors, to achieve more accurate and flexible posterior image distributions.

Key insights

Optimize diffusion priors from a single observation by combining them into a product-of-experts and maximizing Bayesian evidence.

Principles

• True prior distributions are never known in practice.
• Strong priors risk overconfidence; weak priors are less informative.
• Bayesian evidence provides a principled metric for prior selection.

Method

The method involves sampling from a product prior and its corresponding posterior, then using these samples to estimate evidence gradients. Exponents are optimized via grid-based evidence field estimation or generalized EM.

In practice

• Combine GRMHD and generic space priors for black hole imaging.
• Use text-conditioned Stable Diffusion for image deblurring.
• Constrain exponent sums to 1 for latent diffusion models.

Topics

• Diffusion Priors
• Inverse Problems
• Bayesian Evidence
• Product-of-Experts
• Expectation-Maximization

Best for: Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

Related on AIssential

• Exact Posterior Score Estimation for Solving Linear Inverse Problems — For linear Gaussian inverse problems, exact posterior sampling reduces to anisotropic denoising at a measurement-aware shifted pivot.
• Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization — Inverse entropic optimal transport provides a unified likelihood maximization framework for semi-supervised conditional distribution learning using mixed data.
• Bayesian Inference: Overview — Bayesian inference updates prior parameter beliefs with data to yield a posterior distribution, balancing evidence and existing knowledge.
• A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling — A stabilized path-space framework improves diffusion posterior sampling by connecting it to stochastic optimal control and removing bias.
• Leveraging tails for adaptation — Heavier p-exponential prior tails (p→0) significantly improve Bayesian posterior contraction rates, enabling full adaptation to unknown function smoothness.
• Nonparametric Estimation of a Factorizable Density using Diffusion Models — Diffusion models can implicitly estimate factorizable densities, achieving minimax optimal rates.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CV updates on arXiv.org.