# Do we need equivariant models for molecule generation?

arXiv: https://arxiv.org/abs/2507.09753 · HTML: https://mlsanity.com/paper/2507.09753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 13 Jul 2025.

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

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Neural Empirical Bayes](https://mlsanity.com/paper/1903.02334/) (2019)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Learning a Continuous Representation of 3D Molecular Structures with Deep Generative Models](https://mlsanity.com/paper/2010.08687/) (2020)
- [Equivariance versus Augmentation for Spherical Images](https://mlsanity.com/paper/2202.03990/) (2022)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)
- [Emergent Equivariance in Deep Ensembles](https://mlsanity.com/paper/2403.03103/) (2024)
- [Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/2310.08429/) (2023)
- [NEBULA: Neural Empirical Bayes Under Latent Representations for Efficient and Controllable Design of Molecular Libraries](https://mlsanity.com/paper/2407.03428/) (2024)
- [Soft Random Sampling: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2311.12727/) (2023)

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

- [Training Dynamics of Learning 3D-Rotational Equivariance](https://mlsanity.com/paper/2512.02303/) (2025)
- [Balancing Symmetry and Efficiency in Graph Flow Matching](https://mlsanity.com/paper/2602.18084/) (2026)

## Abstract (arXiv)

Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality 3D molecules. However, these models are complex, difficult to train, and scale poorly. We investigate whether non-equivariant convolutional neural networks (CNNs) trained with rotation augmentations can learn equivariance and match the performance of equivariant models. We derive a loss decomposition that separates prediction error from equivariance error, and evaluate how model size, dataset size, and training duration affect performance across denoising, molecule generation, and property prediction. To our knowledge, this is the first study to analyze learned equivariance in generative tasks.