# Recovering molecules from coarse-grained beads: free-energy-conditioned generative backmapping across chemical space

arXiv: https://arxiv.org/abs/2609.04432 · HTML: https://mlsanity.com/paper/2609.04432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 76 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [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)
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- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Conditional molecular design with deep generative models](https://mlsanity.com/paper/1805.00108/) (2018)
- [ChemGAN challenge for drug discovery: can AI reproduce natural chemical diversity?](https://mlsanity.com/paper/1708.08227/) (2017)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [Classifier-free graph diffusion for molecular property targeting](https://mlsanity.com/paper/2312.17397/) (2023)
- [DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces](https://mlsanity.com/paper/2307.12451/) (2023)
- [Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions](https://mlsanity.com/paper/2511.01464/) (2025)
- [Understanding the Quality-Diversity Trade-off in Diffusion Language Models](https://mlsanity.com/paper/2503.10683/) (2025)

## Abstract (arXiv)

Transferable coarse-grained (CG) force fields compress chemical space: by aggregating atoms into a reduced set of interaction beads, models such as MARTINI reduce the number of distinguishable compounds by roughly three orders of magnitude, making high-throughput screening of thermodynamic properties tractable across soft matter, with drug--membrane permeability as a well-developed example. The compression is lossy and, so far, one-way: a screen returns a combination of beads, with no established route back to the compounds it stands for. Recovering those compounds--compositional backmapping--is a one-to-many inverse map, distinct from the better-studied conformational problem of rebuilding atomic coordinates from a known mapping. Here we formulate compositional backmapping as conditional graph generation by introducing juniper, a discrete denoising diffusion model over molecular graphs conditioned on the octanol--water partition free energy Delta GW mapsto O, the principal driver of MARTINI bead type assignment and hence a proxy for bead identity. Trained on molecules of up to 9 heavy atoms mapped onto one or two beads, juniper generates molecules that are 93% valid and 92% unique for two-bead targets, and whose Delta GW mapsto O distributions track the target Delta GCGW mapsto O linearly (r2 ≥ 0.96), departing only in the hydrophobic and hydrophilic tails. Although the model receives no chemical information beyond a single scalar, the functional groups shift systematically with the imposed free energy, from branched hydrocarbons at the apolar end to amides, imides, and isocyanates at the polar end. A bead combination flagged by a CG screen can therefore be turned into candidate molecules for atomistic study or synthesis.