# Score-based diffusion priors for multi-target detection

arXiv: https://arxiv.org/abs/2312.08500 · HTML: https://mlsanity.com/paper/2312.08500/

## 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 18 of its 40 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Fundamental Limits in Multi-image Alignment](https://mlsanity.com/paper/1602.01541/) (2016)
- [Image recovery from rotational and translational invariants](https://mlsanity.com/paper/1910.10006/) (2019)
- [Multi-target Detection with an Arbitrary Spacing Distribution](https://mlsanity.com/paper/1905.03176/) (2019)
- [Two-dimensional multi-target detection: an autocorrelation analysis approach](https://mlsanity.com/paper/2105.06765/) (2021)
- [Expectation-maximization for structure determination directly from cryo-EM micrographs](https://mlsanity.com/paper/2303.02157/) (2023)
- [Multi-target detection with rotations](https://mlsanity.com/paper/2101.07709/) (2021)
- [An approximate expectation-maximization for two-dimensional multi-target detection](https://mlsanity.com/paper/2110.02289/) (2021)

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

- [Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection](https://mlsanity.com/paper/2509.11397/) (2025)

## Abstract (arXiv)

Multi-target detection (MTD) is the problem of estimating an image from a large, noisy measurement that contains randomly translated and rotated copies of the image. Motivated by the single-particle cryo-electron microscopy technology, we design data-driven diffusion priors for the MTD problem, derived from score-based stochastic differential equations models. We then integrate the prior into the approximate expectation-maximization algorithm. In particular, our method alternates between an expectation step that approximates the expected log-likelihood and a maximization step that balances the approximated log-likelihood with the learned log-prior. We show on two datasets that adding the data-driven prior substantially reduces the estimation error, in particular in high noise regimes.