# Generalized Flow Matching for Transition Dynamics Modeling

arXiv: https://arxiv.org/abs/2410.15128 · HTML: https://mlsanity.com/paper/2410.15128/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## 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, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [Generalized Schr"odinger Bridge Matching](https://mlsanity.com/paper/2310.02233/) (2023)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model](https://mlsanity.com/paper/2304.06174/) (2023)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [A reinforcement learning approach to rare trajectory sampling](https://mlsanity.com/paper/2005.12890/) (2020)
- [Neural Optimal Transport with Lagrangian Costs](https://mlsanity.com/paper/2406.00288/) (2024)
- [Reinforcement learning of rare diffusive dynamics](https://mlsanity.com/paper/2105.04321/) (2021)
- [Multitask machine learning of collective variables for enhanced sampling of rare events](https://mlsanity.com/paper/2012.03909/) (2020)
- [React-OT: Optimal Transport for Generating Transition State in Chemical Reactions](https://mlsanity.com/paper/2404.13430/) (2024)

## Built on by (most cited first, 4 of 4)

- [Transferable Learning of Reaction Pathways from Geometric Priors](https://mlsanity.com/paper/2504.15370/) (2025)
- [Riemannian Denoising Model for Molecular Structure Optimization with Chemical Accuracy](https://mlsanity.com/paper/2411.19769/) (2024)
- [A Priori Sampling of Transition States with Guided Diffusion](https://mlsanity.com/paper/2603.25980/) (2026)
- [Stochastic Control Policies for Robust Molecular Transition Path Sampling](https://mlsanity.com/paper/2608.13800/) (2026)

## Abstract (arXiv)

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities. However, the computational challenge often lies on sampling exponentially many paths in which only a small fraction ends in the target metastable state due to existence of high energy barriers. To amortize the cost, we propose a data-driven approach to warm-up the simulation by learning nonlinear interpolations from local dynamics. Specifically, we infer a potential energy function from local dynamics data. To find plausible paths between two metastable states, we formulate a generalized flow matching framework that learns a vector field to sample propable paths between the two marginal densities under the learned energy function. Furthermore, we iteratively refine the model by assigning importance weights to the sampled paths and buffering more likely paths for training. We validate the effectiveness of the proposed method to sample probable paths on both synthetic and real-world molecular systems.