# Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/2606.27818 · HTML: https://mlsanity.com/paper/2606.27818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [Deep Declarative Networks: A New Hope](https://mlsanity.com/paper/1909.04866/) (2019)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [FilterReg: Robust and Efficient Probabilistic Point-Set Registration using Gaussian Filter and Twist Parameterization](https://mlsanity.com/paper/1811.10136/) (2018)
- [TorchOpt: An Efficient Library for Differentiable Optimization](https://mlsanity.com/paper/2211.06934/) (2022)
- [An Adaptive Data Representation for Robust Point-Set Registration and Merging](https://mlsanity.com/paper/1511.04240/) (2015)
- [Analysis of Robust Functions for Registration Algorithms](https://mlsanity.com/paper/1810.01474/) (2018)

## Abstract (arXiv)

We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg-Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.