# Generating valid Euclidean distance matrices

arXiv: https://arxiv.org/abs/1910.03131 · HTML: https://mlsanity.com/paper/1910.03131/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2019.

## Built on by (most cited first, 19 of 19)

- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [Direct Molecular Conformation Generation](https://mlsanity.com/paper/2202.01356/) (2022)
- [An Equivariant Generative Framework for Molecular Graph-Structure Co-Design](https://mlsanity.com/paper/2304.12436/) (2023)
- [Geometry Informed Tokenization of Molecules for Language Model Generation](https://mlsanity.com/paper/2408.10120/) (2024)
- [Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations](https://mlsanity.com/paper/2205.08306/) (2022)
- [SILVR: Guided Diffusion for Molecule Generation](https://mlsanity.com/paper/2304.10905/) (2023)
- [Auto-Encoding Molecular Conformations](https://mlsanity.com/paper/2101.01618/) (2021)
- [Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations](https://mlsanity.com/paper/2106.04464/) (2021)
- [Generating Physical Dynamics under Priors](https://mlsanity.com/paper/2409.00730/) (2024)
- [Text-guided Diffusion Model for 3D Molecule Generation](https://mlsanity.com/paper/2410.03803/) (2024)
- [Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes](https://mlsanity.com/paper/2307.04493/) (2023)
- [On Diffusion Process in SE(3)-invariant Space](https://mlsanity.com/paper/2403.01430/) (2024)
- [Cluster Generation via Deep Energy-Based Model](https://mlsanity.com/paper/2206.09002/) (2022)
- [On Accelerating Diffusion-based Molecular Conformation Generation in SE(3)-invariant Space](https://mlsanity.com/paper/2310.04915/) (2023)

## Abstract (arXiv)

Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an architecture which allows to produce valid Euclidean distance matrices, which by construction are already invariant under rotation and translation of the described object. Motivated by the goal to generate molecular structures in Cartesian space, we use this architecture to construct a Wasserstein GAN utilizing a permutation invariant critic network. This makes it possible to generate molecular structures in a one-shot fashion by producing Euclidean distance matrices which have a three-dimensional embedding.