# Response Matching for generating materials and molecules

arXiv: https://arxiv.org/abs/2405.09057 · HTML: https://mlsanity.com/paper/2405.09057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [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)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [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)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Generating 3D Molecules Conditional on Receptor Binding Sites with Deep Generative Models](https://mlsanity.com/paper/2110.15200/) (2021)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generation](https://mlsanity.com/paper/2305.07508/) (2023)
- [MDM: Molecular Diffusion Model for 3D Molecule Generation](https://mlsanity.com/paper/2209.05710/) (2022)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Cartesian atomic cluster expansion for machine learning interatomic potentials](https://mlsanity.com/paper/2402.07472/) (2024)
- [Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells](https://mlsanity.com/paper/2310.10695/) (2023)

## Built on by (most cited first, 1 of 1)

- [Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials](https://mlsanity.com/paper/2602.22251/) (2026)

## Abstract (arXiv)

Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation, rotation, and periodicity. Here, we present a novel generative method called Response Matching (RM), which leverages the fact that each stable material or molecule exists at the minimum of its potential energy surface. Consequently, any perturbation induces a response in energy and stress, driving the structure back to equilibrium. Matching to such response is closely related to score matching in diffusion models. By employing the combination of a machine learning interatomic potential and random structure search as the denoising model, RM exploits the locality of atomic interactions, and inherently respects permutation, translation, rotation, and periodic invariances. RM is the first model to handle both molecules and bulk materials under the same framework. We demonstrate the efficiency and generalization of RM across three systems: a small organic molecular dataset, stable crystals from the Materials Project, and one-shot learning on a single diamond configuration.