# SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups

arXiv: https://arxiv.org/abs/2607.27431 · HTML: https://mlsanity.com/paper/2607.27431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 11 of 11)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Progressive Distillation for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2202.00512/) (2022)
- [AlphaFlow: Understanding and Improving MeanFlow Models](https://mlsanity.com/paper/2510.20771/) (2025)
- [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)
- [Riemannian Variational Flow Matching for Material and Protein Design](https://mlsanity.com/paper/2502.12981/) (2025)
- [ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation](https://mlsanity.com/paper/2502.14637/) (2025)
- [Riemannian MeanFlow](https://mlsanity.com/paper/2602.07744/) (2026)
- [Riemannian MeanFlow for One-Step Generation on Manifolds](https://mlsanity.com/paper/2603.10718/) (2026)

## Abstract (arXiv)

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference requires numerically integrating an ODE over hundreds of network evaluations, each involving a Lie group exponential map - a bottleneck for high-throughput design campaigns. We introduce SE(3)-MeanFlow, a few-step generative framework that extends MeanFlow from Euclidean space to the Lie group geometry of protein frames. Working natively in the Lie algebra so(3) and in R^3, we derive closed-form average-velocity identities for rotations and translations, giving simulation-free training targets. We further introduce an SE(3) alpha-Flow objective that removes the Jacobian-vector product from the rotation branch and serves as a warm-up stage, after which training switches to a small-t stabilized MeanFlow loss that is used for the remainder of pretraining and for rectification-based post-training. In protein backbone generation, SE(3)-MeanFlow matches or exceeds flow-matching baselines that use several times more sampling steps, and its advantage widens in the few-step regime, where rectification lets it lead at every matched budget - at a modest cost in diversity.