# Factored Levenberg-Marquardt for Diffeomorphic Image Registration: An efficient optimizer for FireANTs

arXiv: https://arxiv.org/abs/2603.19371 · HTML: https://mlsanity.com/paper/2603.19371/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 2 of 2)

- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [Deep Implicit Optimization enables Robust Learnable Features for Deformable Image Registration](https://mlsanity.com/paper/2406.07361/) (2024)

## Abstract (arXiv)

FireANTs introduced a novel Eulerian descent method for plug-and-play behavior with arbitrary optimizers adapted for diffeomorphic image registration as a test-time optimization problem, with a GPU-accelerated implementation. FireANTs uses Adam as its default optimizer for fast and more robust optimization. However, Adam requires storing state variables (i.e. momentum and squared-momentum estimates), each of which can consume significant memory, prohibiting its use for significantly large images. In this work, we propose a modified Levenberg-Marquardt (LM) optimizer that requires only a single scalar damping parameter as optimizer state, that is adaptively tuned using a trust region approach. The resulting optimizer reduces memory by up to 24.6% for large volumes, and retaining performance across all four datasets. A single hyperparameter configuration tuned on brain MRI transfers without modification to lung CT and cross-modal abdominal registration, matching or outperforming Adam on three of four benchmarks. We also perform ablations on the effectiveness of using Metropolis-Hastings style rejection step to prevent updates that worsen the loss function.