# Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration

arXiv: https://arxiv.org/abs/1804.07172 · HTML: https://mlsanity.com/paper/1804.07172/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2018.

## Built on by (most cited first, 23 of 23)

- [DiffuseMorph: Unsupervised Deformable Image Registration Using Diffusion Model](https://mlsanity.com/paper/2112.05149/) (2021)
- [Equitable modelling of brain imaging by counterfactual augmentation with morphologically constrained 3D deep generative models](https://mlsanity.com/paper/2111.14923/) (2021)
- [FSDiffReg: Feature-wise and Score-wise Diffusion-guided Unsupervised Deformable Image Registration for Cardiac Images](https://mlsanity.com/paper/2307.12035/) (2023)
- [Cross-Modality Image Registration using a Training-Time Privileged Third Modality](https://mlsanity.com/paper/2207.12901/) (2022)
- [Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling](https://mlsanity.com/paper/2109.13630/) (2021)
- [SITReg: Multi-resolution architecture for symmetric, inverse consistent, and topology preserving image registration](https://mlsanity.com/paper/2303.10211/) (2023)
- [Medical image registration using unsupervised deep neural network: A scoping literature review](https://mlsanity.com/paper/2208.01825/) (2022)
- [Unsupervised Echocardiography Registration through Patch-based MLPs and Transformers](https://mlsanity.com/paper/2211.11687/) (2022)
- [Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging](https://mlsanity.com/paper/2410.09299/) (2024)
- [MICS : Multi-steps, Inverse Consistency and Symmetric deep learning registration network](https://mlsanity.com/paper/2111.12123/) (2021)
- [Generative Aging of Brain Images with Diffeomorphic Registration](https://mlsanity.com/paper/2205.15607/) (2022)
- [CLAIRE -- Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applications](https://mlsanity.com/paper/2209.08189/) (2022)
- [IdenBAT: Disentangled Representation Learning for Identity-Preserved Brain Age Transformation](https://mlsanity.com/paper/2410.16945/) (2024)
- [Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs](https://mlsanity.com/paper/2506.00947/) (2025)
- [AtlasMorph: Learning conditional deformable templates for brain MRI](https://mlsanity.com/paper/2511.13609/) (2025)
- [InstantGroup: Instant Template Generation for Scalable Group of Brain MRI Registration](https://mlsanity.com/paper/2211.05622/) (2022)
- [Diffeomorphic Transformer-based Abdomen MRI-CT Deformable Image Registration](https://mlsanity.com/paper/2405.02692/) (2024)
- [NestedMorph: Enhancing Deformable Medical Image Registration with Nested Attention Mechanisms](https://mlsanity.com/paper/2410.02550/) (2024)
- [DDR-Net: Dividing and Downsampling Mixed Network for Diffeomorphic Image Registration](https://mlsanity.com/paper/2105.11361/) (2021)
- [Unsupervised diffeomorphic cardiac image registration using parameterization of the deformation field](https://mlsanity.com/paper/2208.13275/) (2022)
- [A Two-Step Deep Learning Method for 3DCT-2DUS Kidney Registration During Breathing](https://mlsanity.com/paper/2305.13855/) (2023)
- [Deep learning motion correction of quantitative stress perfusion cardiovascular magnetic resonance](https://mlsanity.com/paper/2510.00723/) (2025)
- [Dynamic Stream Network for Combinatorial Explosion Problem in Deformable Medical Image Registration](https://mlsanity.com/paper/2512.19486/) (2025)

## Abstract (arXiv)

We propose a deformable registration algorithm based on unsupervised learning of a low-dimensional probabilistic parameterization of deformations. We model registration in a probabilistic and generative fashion, by applying a conditional variational autoencoder (CVAE) network. This model enables to also generate normal or pathological deformations of any new image based on the probabilistic latent space. Most recent learning-based registration algorithms use supervised labels or deformation models, that miss important properties such as diffeomorphism and sufficiently regular deformation fields. In this work, we constrain transformations to be diffeomorphic by using a differentiable exponentiation layer with a symmetric loss function. We evaluated our method on 330 cardiac MR sequences and demonstrate robust intra-subject registration results comparable to two state-of-the-art methods but with more regular deformation fields compared to a recent learning-based algorithm. Our method reached a mean DICE score of 78.3% and a mean Hausdorff distance of 7.9mm. In two preliminary experiments, we illustrate the model's abilities to transport pathological deformations to healthy subjects and to cluster five diseases in the unsupervised deformation encoding space with a classification performance of 70%.