  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.
