# Reflection-Equivariant Diffusion for 3D Structure Determination from Isotopologue Rotational Spectra in Natural Abundance

arXiv: https://arxiv.org/abs/2310.11609 · HTML: https://mlsanity.com/paper/2310.11609/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 82 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [On the adequacy of untuned warmup for adaptive optimization](https://mlsanity.com/paper/1910.04209/) (2019)
- [ResiDual: Transformer with Dual Residual Connections](https://mlsanity.com/paper/2304.14802/) (2023)

## Built on by (most cited first, 2 of 2)

- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Twins in rotational spectroscopy: Does a rotational spectrum uniquely identify a molecule?](https://mlsanity.com/paper/2404.04225/) (2024)

## Abstract (arXiv)

Structure determination is necessary to identify unknown organic molecules, such as those in natural products, forensic samples, the interstellar medium, and laboratory syntheses. Rotational spectroscopy enables structure determination by providing accurate 3D information about small organic molecules via their moments of inertia. Using these moments, Kraitchman analysis determines isotopic substitution coordinates, which are the unsigned |x|,|y|,|z| coordinates of all atoms with natural isotopic abundance, including carbon, nitrogen, and oxygen. While unsigned substitution coordinates can verify guesses of structures, the missing +/- signs make it challenging to determine the actual structure from the substitution coordinates alone. To tackle this inverse problem, we develop KREED (Kraitchman REflection-Equivariant Diffusion), a generative diffusion model that infers a molecule's complete 3D structure from its molecular formula, moments of inertia, and unsigned substitution coordinates of heavy atoms. KREED's top-1 predictions identify the correct 3D structure with >98% accuracy on the QM9 and GEOM datasets when provided with substitution coordinates of all heavy atoms with natural isotopic abundance. When substitution coordinates are restricted to only a subset of carbons, accuracy is retained at 91% on QM9 and 32% on GEOM. On a test set of experimentally measured substitution coordinates gathered from the literature, KREED predicts the correct all-atom 3D structure in 25 of 33 cases, demonstrating experimental applicability for context-free 3D structure determination with rotational spectroscopy.