# Molecular relaxation by reverse diffusion with time step prediction

arXiv: https://arxiv.org/abs/2404.10935 · HTML: https://mlsanity.com/paper/2404.10935/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 141 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## Builds on (most cited first, 30 of 45)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)

## Built on by (most cited first, 9 of 9)

- [Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features](https://mlsanity.com/paper/2408.17198/) (2024)
- [Noise Scheduling as Information-Guided Allocation in Diffusion Training](https://mlsanity.com/paper/2602.18647/) (2026)
- [Conditional Synthesis of 3D Molecules with Time Correction Sampler](https://mlsanity.com/paper/2411.00551/) (2024)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [Disentangling Total-Variance and Signal-to-Noise-Ratio Improves Diffusion Models](https://mlsanity.com/paper/2502.08598/) (2025)
- [Bridging Geometric States via Geometric Diffusion Bridge](https://mlsanity.com/paper/2410.24220/) (2024)
- [Riemannian Denoising Model for Molecular Structure Optimization with Chemical Accuracy](https://mlsanity.com/paper/2411.19769/) (2024)
- [Generative Pseudo-Force Fields for Molecular Generation](https://mlsanity.com/paper/2605.19050/) (2026)
- [Information-geometric adaptive sampling for graph diffusion](https://mlsanity.com/paper/2605.00250/) (2026)

## Abstract (arXiv)

Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.