# ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation

arXiv: https://arxiv.org/abs/2502.14637 · HTML: https://mlsanity.com/paper/2502.14637/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Generating Novel, Designable, and Diverse Protein Structures by Equivariantly Diffusing Oriented Residue Clouds](https://mlsanity.com/paper/2301.12485/) (2023)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generation](https://mlsanity.com/paper/2405.20313/) (2024)
- [Out of Many, One: Designing and Scaffolding Proteins at the Scale of the Structural Universe with Genie 2](https://mlsanity.com/paper/2405.15489/) (2024)
- [Quaternion kinematics for the error-state Kalman filter](https://mlsanity.com/paper/1711.02508/) (2017)
- [Rigid Body Flows for Sampling Molecular Crystal Structures](https://mlsanity.com/paper/2301.11355/) (2023)
- [Large Language-Geometry Model: When LLM meets Equivariance](https://mlsanity.com/paper/2502.11149/) (2025)
- [Quaternion Product Units for Deep Learning on 3D Rotation Groups](https://mlsanity.com/paper/1912.07791/) (2019)
- [Generating Highly Designable Proteins with Geometric Algebra Flow Matching](https://mlsanity.com/paper/2411.05238/) (2024)

## Built on by (most cited first, 11 of 11)

- [Riemannian Consistency Model](https://mlsanity.com/paper/2510.00983/) (2025)
- [OAT-FM: Optimal Acceleration Transport for Improved Flow Matching](https://mlsanity.com/paper/2509.24936/) (2025)
- [Constrained Diffusion for Protein Design with Hard Structural Constraints](https://mlsanity.com/paper/2510.14989/) (2025)
- [PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models](https://mlsanity.com/paper/2504.08859/) (2025)
- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [Geometric Mixture Models for Electrolyte Conductivity Prediction](https://mlsanity.com/paper/2510.15403/) (2025)
- [Flows, straight but not so fast: Exploring the design space of Rectified Flows in Protein Design](https://mlsanity.com/paper/2510.24732/) (2025)
- [MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization](https://mlsanity.com/paper/2602.11189/) (2026)
- [SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups](https://mlsanity.com/paper/2607.27431/) (2026)
- [Protein Structure Prediction: From Evolutionary Constraints to Generative Modeling](https://mlsanity.com/paper/2608.16094/) (2026)
- [CQF-HMR: Continuous Quaternion Flows for Probabilistic 3D Human Mesh Recovery from a Single Image](https://mlsanity.com/paper/2609.00995/) (2026)

## Abstract (arXiv)

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves on-par performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37x faster than RFDiffusion and 63x faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency. The code is available at https://github.com/AngxiaoYue/ReQFlow.