# Posterior samples of source galaxies in strong gravitational lenses with score-based priors

arXiv: https://arxiv.org/abs/2211.03812 · HTML: https://mlsanity.com/paper/2211.03812/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Deep Generative Stochastic Networks Trainable by Backprop](https://mlsanity.com/paper/1306.1091/) (2013)
- [Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net](https://mlsanity.com/paper/1711.02282/) (2017)
- [Realistic galaxy image simulation via score-based generative models](https://mlsanity.com/paper/2111.01713/) (2021)
- [AR-DAE: Towards Unbiased Neural Entropy Gradient Estimation](https://mlsanity.com/paper/2006.05164/) (2020)
- [Probabilistic Mass Mapping with Neural Score Estimation](https://mlsanity.com/paper/2201.05561/) (2022)
- [Strong Lensing Source Reconstruction Using Continuous Neural Fields](https://mlsanity.com/paper/2206.14820/) (2022)

## Built on by (most cited first, 20 of 20)

- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior](https://mlsanity.com/paper/2309.01949/) (2023)
- [Improving Gradient-guided Nested Sampling for Posterior Inference](https://mlsanity.com/paper/2312.03911/) (2023)
- [Blind Inversion using Latent Diffusion Priors](https://mlsanity.com/paper/2407.01027/) (2024)
- [Diffusion Models for Probabilistic Deconvolution of Galaxy Images](https://mlsanity.com/paper/2307.11122/) (2023)
- [Bayesian Imaging for Radio Interferometry with Score-Based Priors](https://mlsanity.com/paper/2311.18012/) (2023)
- [Echoes in the Noise: Posterior Samples of Faint Galaxy Surface Brightness Profiles with Score-Based Likelihoods and Priors](https://mlsanity.com/paper/2311.18002/) (2023)
- [A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fields](https://mlsanity.com/paper/2505.13189/) (2025)
- [Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models](https://mlsanity.com/paper/2511.04792/) (2025)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems](https://mlsanity.com/paper/2405.15643/) (2024)
- [MIRA: A Score for Conditional Distribution Accuracy and Model Comparison](https://mlsanity.com/paper/2605.02014/) (2026)
- [ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imaging](https://mlsanity.com/paper/2606.21099/) (2026)
- [Solving Bayesian inverse problems with diffusion priors and off-policy RL](https://mlsanity.com/paper/2503.09746/) (2025)
- [Variance-Reduced Diffusion Sampling via Target Score Identity](https://mlsanity.com/paper/2601.01594/) (2026)

## Abstract (arXiv)

Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data.