# Differentiable Score-Based Likelihoods: Learning CT Motion Compensation From Clean Images

arXiv: https://arxiv.org/abs/2404.14747 · HTML: https://mlsanity.com/paper/2404.14747/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 20 of 20)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Diffusion Models for Medical Anomaly Detection](https://mlsanity.com/paper/2203.04306/) (2022)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Improving Reconstruction Autoencoder Out-of-distribution Detection with Mahalanobis Distance](https://mlsanity.com/paper/1812.02765/) (2018)
- [Rethinking Reconstruction Autoencoder-Based Out-of-Distribution Detection](https://mlsanity.com/paper/2203.02194/) (2022)
- [Unsupervised 3D out-of-distribution detection with latent diffusion models](https://mlsanity.com/paper/2307.03777/) (2023)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.17432/) (2023)
- [Projection Regret: Reducing Background Bias for Novelty Detection via Diffusion Models](https://mlsanity.com/paper/2312.02615/) (2023)
- [Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction](https://mlsanity.com/paper/2212.02177/) (2022)
- [Appearance Learning for Image-based Motion Estimation in Tomography](https://mlsanity.com/paper/2006.10390/) (2020)
- [A gradient-based approach to fast and accurate head motion compensation in cone-beam CT](https://mlsanity.com/paper/2401.09283/) (2024)
- [Confidence-Aware and Self-Supervised Image Anomaly Localisation](https://mlsanity.com/paper/2303.13227/) (2023)
- [Inertial Measurements for Motion Compensation in Weight-bearing Cone-beam CT of the Knee](https://mlsanity.com/paper/2007.04655/) (2020)

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

- [Revisiting Pose Sensitivity in Splat-based Computed Tomography under Sparse-view Reconstruction](https://mlsanity.com/paper/2608.04752/) (2026)

## Abstract (arXiv)

Motion artifacts can compromise the diagnostic value of computed tomography (CT) images. Motion correction approaches require a per-scan estimation of patient-specific motion patterns. In this work, we train a score-based model to act as a probability density estimator for clean head CT images. Given the trained model, we quantify the deviation of a given motion-affected CT image from the ideal distribution through likelihood computation. We demonstrate that the likelihood can be utilized as a surrogate metric for motion artifact severity in the CT image facilitating the application of an iterative, gradient-based motion compensation algorithm. By optimizing the underlying motion parameters to maximize likelihood, our method effectively reduces motion artifacts, bringing the image closer to the distribution of motion-free scans. Our approach achieves comparable performance to state-of-the-art methods while eliminating the need for a representative data set of motion-affected samples. This is particularly advantageous in real-world applications, where patient motion patterns may exhibit unforeseen variability, ensuring robustness without implicit assumptions about recoverable motion types.