# ReCurveflow: A Flow Matching Framework that Learns Curved Reaction Trajectories to Predict Transition State Geometries

arXiv: https://arxiv.org/abs/2608.20869 · HTML: https://mlsanity.com/paper/2608.20869/

## 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 9 of its 21 references that are in the map.
- First posted on arXiv 21 Aug 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, 9 of 9)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model](https://mlsanity.com/paper/2304.06174/) (2023)
- [Diffusion-based Generative AI for Exploring Transition States from 2D Molecular Graphs](https://mlsanity.com/paper/2304.12233/) (2023)
- [SOAR: Self-Correction for Optimal Alignment and Refinement in Diffusion Models](https://mlsanity.com/paper/2604.12617/) (2026)
- [Exposure Bias Can Alleviate Itself via Directional and Frequency Rectification in Flow Matching](https://mlsanity.com/paper/2606.28226/) (2026)
- [FragmentFlow: Scalable Transition State Generation for Large Molecules](https://mlsanity.com/paper/2602.02310/) (2026)

## Abstract (arXiv)

Predicting transition states (TS) in chemical reactions is crucial, as they provide insights into reaction mechanisms. Recent work on TS prediction have focused on flow matching supervised on straight linear paths that do not align with actual reaction trajectories. We propose a novel flow matching-based framework ReCurveflow that learns to predict TS geometries supervised on continuously curved reference paths interpolated from a full NEB-derived band of molecular geometries. We also introduce off-path correction, which grants ReCurveflow with the ability to produce corrective velocity fields when engaged off-path geometry states during inference rollout, leading to better resistance against exposure bias and accuracy in TS prediction. Across three data splits and six evaluation metrics, ReCurveflow achieves the best result on the majority of split-metric combinations against seven baselines. Qualitative analyses further show that ReCurveflow generates reaction trajectories with energy profiles that closely track the reference NEB path, provides initializations that ease the NEB optimization bottleneck, and exhibits the intended corrective behavior in its learned velocity fields. The ReCurveflow codebase is publicly available at https://github.com/dmis-lab/ReCurveflow.