# RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations

arXiv: https://arxiv.org/abs/2305.12854 · HTML: https://mlsanity.com/paper/2305.12854/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 96 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 30 of 45)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Metrics for Deep Generative Models](https://mlsanity.com/paper/1711.01204/) (2017)
- [Networks for Joint Affine and Non-parametric Image Registration](https://mlsanity.com/paper/1903.08811/) (2019)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [DeepFLASH: An Efficient Network for Learning-based Medical Image Registration](https://mlsanity.com/paper/2004.02097/) (2020)
- [Potential Flow Generator with L2 Optimal Transport Regularity for Generative Models](https://mlsanity.com/paper/1908.11462/) (2019)
- [Metric Learning for Image Registration](https://mlsanity.com/paper/1904.09524/) (2019)
- [Fast and Robust Shortest Paths on Manifolds Learned from Data](https://mlsanity.com/paper/1901.07229/) (2019)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)

## Built on by (most cited first, 7 of 7)

- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [RONOM: Reduced-Order Neural Operator Modeling](https://mlsanity.com/paper/2507.12814/) (2025)
- [Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators](https://mlsanity.com/paper/2509.26371/) (2025)
- [Joint Manifold Learning and Optimal Transport for Dynamic Imaging](https://mlsanity.com/paper/2505.11913/) (2025)
- [Shape Modeling of Longitudinal Medical Images: From Diffeomorphic Metric Mapping to Deep Learning](https://mlsanity.com/paper/2503.21489/) (2025)
- [An Elastic Shape Variational Autoencoder for Skeleton Pose Trajectories](https://mlsanity.com/paper/2605.09231/) (2026)
- [ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learning](https://mlsanity.com/paper/2606.06887/) (2026)

## Abstract (arXiv)

Diffeomorphic registration frameworks such as Large Deformation Diffeomorphic Metric Mapping (LDDMM) are used in computer graphics and the medical domain for atlas building, statistical latent modeling, and pairwise and groupwise registration. In recent years, researchers have developed neural network-based approaches regarding diffeomorphic registration to improve the accuracy and computational efficiency of traditional methods. In this work, we focus on a limitation of neural network-based atlas building and statistical latent modeling methods, namely that they either are (i) resolution dependent or (ii) disregard any data- or problem-specific geometry needed for proper mean-variance analysis. In particular, we overcome this limitation by designing a novel encoder based on resolution-independent implicit neural representations. The encoder achieves resolution invariance for LDDMM-based statistical latent modeling. Additionally, the encoder adds LDDMM Riemannian geometry to resolution-independent deep learning models for statistical latent modeling. We investigate how the Riemannian geometry improves latent modeling and is required for a proper mean-variance analysis. To highlight the benefit of resolution independence for LDDMM-based data variability modeling, we show that our approach outperforms current neural network-based LDDMM latent code models. Our work paves the way for more research into how Riemannian geometry, shape respectively image analysis, and deep learning can be combined.