# Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data

arXiv: https://arxiv.org/abs/2504.20940 · HTML: https://mlsanity.com/paper/2504.20940/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 96 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 30 of 37)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Normalizing flows for atomic solids](https://mlsanity.com/paper/2111.08696/) (2021)
- [Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization](https://mlsanity.com/paper/2006.10343/) (2020)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Amortized Inference Regularization](https://mlsanity.com/paper/1805.08913/) (2018)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers](https://mlsanity.com/paper/2502.06685/) (2025)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [Efficient mapping of phase diagrams with conditional Boltzmann Generators](https://mlsanity.com/paper/2406.12378/) (2024)

## Built on by (most cited first, 2 of 2)

- [Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials](https://mlsanity.com/paper/2510.11148/) (2025)
- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)

## Abstract (arXiv)

Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations (MD), but conventional approaches depend heavily on long all-atom MD trajectories to adequately sample configurational space. This data dependence limits accuracy and generalizability, as unvisited configurations remain excluded from the resulting CG models. We introduce a fully data-free, generative framework for CG that directly targets the all-atom Boltzmann distribution. The model defines a structured latent space comprising slow collective variables, associated with multimodal marginal densities capturing metastable states, and fast variables, represented through simple, unimodal conditional distributions. A learnable, bijective map from latent space to atomistic coordinates enables the automatic and accurate reconstruction of molecular structures. Training relies solely on the interatomic potential and minimizes the reverse Kullback-Leibler (KL) divergence via an energy-based objective. To stabilize optimization and ensure mode coverage, we employ an adaptive tempering scheme that promotes the exploration of diverse configurations. Once trained, the model can generate independent, one-shot equilibrium samples at full atomic resolution. Validation on two synthetic systems, a double-well potential and a Gaussian mixture model, as well as on the benchmark alanine dipeptide, demonstrates that the method captures all relevant modes of the Boltzmann distribution, reconstructs atomic configurations, and automatically learns physically meaningful CG representations. These results suggest a promising, data-free alternative to traditional CG techniques, offering both a principled approach to addressing the long-standing "chicken-and-egg" challenge in coarse-graining and an effective solution to the back-mapping problem by enabling accurate reconstruction of all-atom configurations.