# ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation

arXiv: https://arxiv.org/abs/2410.22388 · HTML: https://mlsanity.com/paper/2410.22388/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 74 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)

## Built on by (most cited first, 30 of 43)

- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction](https://mlsanity.com/paper/2505.18817/) (2025)
- [Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems](https://mlsanity.com/paper/2508.09156/) (2025)
- [Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior](https://mlsanity.com/paper/2509.01543/) (2025)
- [Efficient Flow Matching using Latent Variables](https://mlsanity.com/paper/2505.04486/) (2025)
- [Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching](https://mlsanity.com/paper/2506.07199/) (2025)
- [Sampling 3D Molecular Conformers with Diffusion Transformers](https://mlsanity.com/paper/2506.15378/) (2025)
- [Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion](https://mlsanity.com/paper/2502.09890/) (2025)
- [SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modeling](https://mlsanity.com/paper/2507.11818/) (2025)
- [Disentangling Total-Variance and Signal-to-Noise-Ratio Improves Diffusion Models](https://mlsanity.com/paper/2502.08598/) (2025)
- [Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow](https://mlsanity.com/paper/2507.09785/) (2025)
- [Energy-Based Flow Matching for Generating 3D Molecular Structure](https://mlsanity.com/paper/2508.18949/) (2025)
- [MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching](https://mlsanity.com/paper/2512.12198/) (2025)
- [PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models](https://mlsanity.com/paper/2504.08859/) (2025)
- [Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems](https://mlsanity.com/paper/2508.12569/) (2025)
- [Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition](https://mlsanity.com/paper/2605.25577/) (2026)
- [Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2506.06305/) (2025)
- [AbFlow : End-to-end Paratope-Centric Antibody Design by Interaction Enhanced Flow Matching](https://mlsanity.com/paper/2602.07084/) (2026)
- [A Unified Density Operator View of Flow Control and Merging](https://mlsanity.com/paper/2602.08012/) (2026)
- [Riemannian Denoising Model for Molecular Structure Optimization with Chemical Accuracy](https://mlsanity.com/paper/2411.19769/) (2024)
- [Self-Refining Training for Amortized Density Functional Theory](https://mlsanity.com/paper/2506.01225/) (2025)
- [READ: A Retrieval-Alignment Diffusion Framework for Structure-based Drug Design](https://mlsanity.com/paper/2506.14488/) (2025)
- [GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2507.09043/) (2025)
- [Flow-Matching Based Refiner for Molecular Conformer Generation](https://mlsanity.com/paper/2510.04878/) (2025)
- [Boltzmann Generators for Condensed Matter via Riemannian Flow Matching](https://mlsanity.com/paper/2602.18482/) (2026)
- [FlashMol: High-Quality Molecule Generation in as Few as Four Steps](https://mlsanity.com/paper/2605.07020/) (2026)
- [Vilya-1: An all-atom foundation model for macrocycle structure prediction and design](https://mlsanity.com/paper/2607.09998/) (2026)
- [Discriminative protein sequence modelling with Latent Space Diffusion](https://mlsanity.com/paper/2503.18551/) (2025)
- [polyGen: A Learning Framework for Atomic-level Polymer Structure Generation](https://mlsanity.com/paper/2504.17656/) (2025)

## Abstract (arXiv)

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models that diffuse over conformer fields, or use computationally expensive methods to generate initial structures and diffuse over torsion angles. In this work, we introduce Equivariant Transformer Flow (ET-Flow). We showcase that a well-designed flow matching approach with equivariance and harmonic prior alleviates the need for complex internal geometry calculations and large architectures, contrary to the prevailing methods in the field. Our approach results in a straightforward and scalable method that directly operates on all-atom coordinates with minimal assumptions. With the advantages of equivariance and flow matching, ET-Flow significantly increases the precision and physical validity of the generated conformers, while being a lighter model and faster at inference. Code is available https://github.com/shenoynikhil/ETFlow.