# Optimizing Diffusion Priors in Image Reconstruction from a Single Observation

arXiv: https://arxiv.org/abs/2604.21066 · HTML: https://mlsanity.com/paper/2604.21066/

## Key facts

- Cited by 1 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 43 references that are in the map.
- First posted on arXiv 22 Apr 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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data](https://mlsanity.com/paper/2404.10177/) (2024)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations](https://mlsanity.com/paper/2407.01014/) (2024)
- [Image Reconstruction without Explicit Priors](https://mlsanity.com/paper/2303.12217/) (2023)
- [Think Twice Before You Act: Improving Inverse Problem Solving With MCMC](https://mlsanity.com/paper/2409.08551/) (2024)
- [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)
- [Temporal Score Rescaling for Temperature Sampling in Diffusion and Flow Models](https://mlsanity.com/paper/2510.01184/) (2025)
- [Product of Experts for Visual Generation](https://mlsanity.com/paper/2506.08894/) (2025)
- [Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems](https://mlsanity.com/paper/2407.17667/) (2024)
- [Sample-efficient evidence estimation of score based priors for model selection](https://mlsanity.com/paper/2602.20549/) (2026)

## Built on by (most cited first, 1 of 1)

- [Evidence-Aligned Local Composition of Discrete Experts for Sequence Restoration](https://mlsanity.com/paper/2609.05801/) (2026)

## Abstract (arXiv)

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources. Current approaches to finetuning diffusion models rely on a large number of observations with varying forward operators, which can be difficult to collect for many applications, and thus lead to overfitting when the measurement set is small. We propose a method for tuning a prior from only a single observation by combining existing diffusion priors into a single product-of-experts prior and identifying the exponents that maximize the Bayesian evidence. We validate our method on real-world inverse problems, including black hole imaging, where the true prior is unknown a priori, and image deblurring with text-conditioned priors. We find that the evidence is often maximized by priors that extend beyond those trained on a single dataset. By generalizing the prior through exponent weighting, our approach enables posterior sampling from both tempered and combined diffusion models, yielding more flexible priors that improve the trustworthiness of the resulting posterior image distribution.