# Conditional Normalizing Flows for Active Learning of Coarse-Grained Molecular Representations

arXiv: https://arxiv.org/abs/2402.01195 · HTML: https://mlsanity.com/paper/2402.01195/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Normalizing Flows on Tori and Spheres](https://mlsanity.com/paper/2002.02428/) (2020)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [SE(3) Equivariant Augmented Coupling Flows](https://mlsanity.com/paper/2308.10364/) (2023)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Free-form Flows: Make Any Architecture a Normalizing Flow](https://mlsanity.com/paper/2310.16624/) (2023)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Designing losses for data-free training of normalizing flows on Boltzmann distributions](https://mlsanity.com/paper/2301.05475/) (2023)
- [A Method to Model Conditional Distributions with Normalizing Flows](https://mlsanity.com/paper/1911.02052/) (2019)
- [Invertible Coarse Graining with Physics-Informed Generative Artificial Intelligence](https://mlsanity.com/paper/2305.01243/) (2023)

## Built on by (most cited first, 5 of 5)

- [Temperature-Annealed Boltzmann Generators](https://mlsanity.com/paper/2501.19077/) (2025)
- [Learning Boltzmann Generators via Constrained Mass Transport](https://mlsanity.com/paper/2510.18460/) (2025)
- [End-To-End Learning of Gaussian Mixture Priors for Diffusion Sampler](https://mlsanity.com/paper/2503.00524/) (2025)
- [Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularization](https://mlsanity.com/paper/2602.03729/) (2026)
- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)

## Abstract (arXiv)

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been used to learn the Boltzmann distribution directly, without samples. However, this approach is susceptible to mode collapse and thus often does not explore the full configurational space. In this work, we address this challenge by separating the problem into two levels, the fine-grained and coarse-grained degrees of freedom. A normalizing flow conditioned on the coarse-grained space yields a probabilistic connection between the two levels. To explore the configurational space, we employ coarse-grained simulations with active learning which allows us to update the flow and make all-atom potential energy evaluations only when necessary. Using alanine dipeptide as an example, we show that our methods obtain a speedup to molecular dynamics simulations of approximately 15.9 to 216.2 compared to the speedup of 4.5 of the current state-of-the-art machine learning approach.