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ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation
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Proposes ReQFlow, a quaternion-based SLERP flow-matching model with rectified flow for fast, high-designability protein backbone generation.
Problem
Protein backbone generation with diffusion/flow models suffers from poor designability, especially for long chains, and requires many sampling steps and long inference time.
Approach
Represent each residue's rotation as a unit quaternion and build the rotation flow with exponential-format SLERP (numerically stable near angle 0 or pi), train QFlow matching on SO(3) and R^3 flows, then rectify the flow by retraining on model-generated noise-sample pairs to allow fewer sampling steps.
Key results
- ReQFlow reaches Fraction 0.972 and scRMSD 1.071 at 500 steps on PDB at length 300, versus 0.904 for RFDiffusion and 0.908 for Genie2.
- ReQFlow achieves Fraction 0.912 with 50 steps in 1.78 s, reported as 37x faster than RFDiffusion and 63x faster than Genie2 at length 300.
- On SCOPe, ReQFlow at 500 steps reaches Fraction up to 0.955 across checkpoints, and QFlow/ReQFlow beat FrameFlow/ReFrameFlow in designability at all step counts.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add flow rectification to FrameFlow | FrameFlow on SCOPe · SCOPe | Fraction: 0.880 -> 0.933 | Helped |
| Add flow rectification and filtered self-generated data to QFlow (ablation) | QFlow on PDB · PDB, length 300, 500 steps | Fraction: 0.910_{\pm\text{0.029}} -> 0.969_{\pm\text{0.027}} | Helped |
| Add flow rectification and filtered self-generated data to QFlow (ablation) | QFlow on PDB · PDB, length 300, 50 steps | Fraction: 0.795_{\pm\text{0.051}} -> 0.932_{\pm\text{0.022}} | Helped |
| Filter generated data used for flow rectification (ablation) | ReQFlow on PDB · PDB, length 300, 500 steps | Fraction: 0.612_{\pm\text{0.084}} -> 0.969_{\pm\text{0.027}} | Helped |
| Filter generated data used for flow rectification (ablation) | ReQFlow on PDB · PDB, length 300, 50 steps | Fraction: 0.519_{\pm\text{0.154}} -> 0.932_{\pm\text{0.022}} | Helped |
| Add the exponential step size scheduler (ablation) | QFlow on PDB · PDB, length 300, 500 steps | Fraction: 0.143_{\pm\text{0.079}} -> 0.910_{\pm\text{0.029}} | Helped |
| Add the exponential step size scheduler (ablation) | QFlow on PDB · PDB, length 300, 50 steps | Fraction: 0.047_{\pm\text{0.030}} -> 0.795_{\pm\text{0.051}} | Helped |
| Reduce sampling steps from 500 to 50 (ablation) | ReQFlow on PDB · PDB | Fraction: 0.972 -> 0.912 | Hurt |
| Reduce sampling steps from 500 to 20 (ablation) | ReQFlow on PDB · PDB | Fraction: 0.972 -> 0.872 | Hurt |
| Use ReQFlow instead of QFlow | Quaternion flow on PDB · PDB | Fraction: 0.936 -> 0.972 | Helped |
| Use quaternion flow instead of FrameFlow | Flow model on PDB · PDB | Fraction: 0.872 -> 0.936 | Helped |
| Use quaternion flow instead of FrameFlow | Flow model on SCOPe · SCOPe | Fraction: 0.880 -> 0.899 | Helped |
Surprising findings
- Without data filtering, flow rectification degraded ReQFlow Fraction (0.969 to 0.612 at 500 steps), indicating rectification on low-quality self-generated data hurts.
Limitations
- Long-chain designability relies on a training set limited to 512 residues; performance beyond that is not guaranteed.
- Rectification needs a large set of self-generated samples and careful data filtering with scRMSD and TM-score criteria.
- Diversity and novelty are only competitive, not best, among the compared methods.
Experimental setup
Datasets: PDB SCOPe
Benchmarks: PDB SCOPe
Metrics: Fraction (designability) scRMSD diversity TM-score novelty TM-score inference time
Baselines: RFDiffusion Genie2 FrameDiff FoldFlow FoldFlow2 FrameFlow
Builds on: FrameFlow rectified flow AlphaFold2 FoldFlow
Closest papers by meaning
- SE(3)-Stochastic Flow Matching for Protein Backbone Generation (ICLR 2024 · similarity 0.89)
- Generating Highly Designable Proteins with Geometric Algebra Flow Matching (NeurIPS 2024 · similarity 0.89)
- Proteina: Scaling Flow-based Protein Structure Generative Models (ICLR 2025 · similarity 0.88)
- Learning conformational ensembles of proteins based on backbone geometry (NeurIPS 2025 · similarity 0.87)
- Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Generation (NeurIPS 2024 · similarity 0.87)
- ProtPainter: Draw or Drag Protein via Topology-guided Diffusion (ICLR 2025 · similarity 0.87)
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