# Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths

arXiv: https://arxiv.org/abs/2207.02149 · HTML: https://mlsanity.com/paper/2207.02149/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [Adaptive importance sampling for control and inference](https://mlsanity.com/paper/1505.01874/) (2015)
- [Reinforcement learning of rare diffusive dynamics](https://mlsanity.com/paper/2105.04321/) (2021)
- [Path Integral Control and State Dependent Feedback](https://mlsanity.com/paper/1406.4026/) (2014)
- [Transferable neural networks for enhanced sampling of protein dynamics](https://mlsanity.com/paper/1801.00636/) (2018)
- [Multitask machine learning of collective variables for enhanced sampling of rare events](https://mlsanity.com/paper/2012.03909/) (2020)

## Built on by (most cited first, 30 of 38)

- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [RB-Modulation: Training-Free Personalization of Diffusion Models using Stochastic Optimal Control](https://mlsanity.com/paper/2405.17401/) (2024)
- [Stochastic Optimal Control Matching](https://mlsanity.com/paper/2312.02027/) (2023)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional](https://mlsanity.com/paper/2504.18506/) (2025)
- [Temperature-Annealed Boltzmann Generators](https://mlsanity.com/paper/2501.19077/) (2025)
- [Value Gradient Guidance for Flow Matching Alignment](https://mlsanity.com/paper/2512.05116/) (2025)
- [A Taxonomy of Loss Functions for Stochastic Optimal Control](https://mlsanity.com/paper/2410.00345/) (2024)
- [Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplers](https://mlsanity.com/paper/2405.19961/) (2024)
- [Transition Path Sampling with Boltzmann Generator-based MCMC Moves](https://mlsanity.com/paper/2312.05340/) (2023)
- [The Spacetime of Diffusion Models: An Information Geometry Perspective](https://mlsanity.com/paper/2505.17517/) (2025)
- [Reinforced sequential Monte Carlo for amortised sampling](https://mlsanity.com/paper/2510.11711/) (2025)
- [Control Consistency Losses for Diffusion Bridges](https://mlsanity.com/paper/2512.05070/) (2025)
- [Conditional Lagrangian Wasserstein Flow for Time Series Imputation](https://mlsanity.com/paper/2410.07550/) (2024)
- [Generalized Flow Matching for Transition Dynamics Modeling](https://mlsanity.com/paper/2410.15128/) (2024)
- [React-OT: Optimal Transport for Generating Transition State in Chemical Reactions](https://mlsanity.com/paper/2404.13430/) (2024)
- [An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Control](https://mlsanity.com/paper/2410.05163/) (2024)
- [Simulation-Free Differential Dynamics through Neural Conservation Laws](https://mlsanity.com/paper/2506.18604/) (2025)
- [A unified perspective on fine-tuning and sampling with diffusion and flow models](https://mlsanity.com/paper/2605.00229/) (2026)
- [Estimating Reaction Barriers with Deep Reinforcement Learning](https://mlsanity.com/paper/2407.12453/) (2024)
- [Entangled Schr"odinger Bridge Matching](https://mlsanity.com/paper/2511.07406/) (2025)
- [One-Step Diffusion Samplers via Self-Distillation and Deterministic Flow](https://mlsanity.com/paper/2512.05251/) (2025)
- [Analytic Bridge Diffusions for Controlled Path Generation](https://mlsanity.com/paper/2605.02961/) (2026)
- [A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2606.12710/) (2026)
- [Control, Transport and Sampling: Towards Better Loss Design](https://mlsanity.com/paper/2405.13731/) (2024)
- [Consensus Based Stochastic Control](https://mlsanity.com/paper/2501.17801/) (2025)
- [Single-Step Consistent Diffusion Samplers](https://mlsanity.com/paper/2502.07579/) (2025)
- [Follow the MEP: Scalable Neural Representations for Minimum-Energy Path Discovery in Molecular Systems](https://mlsanity.com/paper/2504.16381/) (2025)

## Abstract (arXiv)

We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy barriers separating the states, these transition paths are unlikely to be sampled with standard Molecular Dynamics (MD) simulation. Traditional methods to augment MD with a bias potential to increase the probability of the transition rely on a dimensionality reduction step based on Collective Variables (CVs). Unfortunately, selecting appropriate CVs requires chemical intuition and traditional methods are therefore not always applicable to larger systems. Additionally, when incorrect CVs are used, the bias potential might not be minimal and bias the system along dimensions irrelevant to the transition. Showing a formal relation between the problem of sampling molecular transition paths, the Schr"odinger bridge problem and stochastic optimal control with neural network policies, we propose a machine learning method for sampling said transitions. Unlike previous non-machine learning approaches our method, named PIPS, does not depend on CVs. We show that our method successful generates low energy transitions for Alanine Dipeptide as well as the larger Polyproline and Chignolin proteins.