Iterated Denoising Energy Matching for Sampling from Boltzmann Densities
Tara Akhound-Sadegh Jarrid Rector-Brooks Avishek Joey Bose Sarthak Mittal Pablo Lemos Cheng-Hao Liu Marcin Sendera Siamak Ravanbakhsh Gauthier Gidel Yoshua Bengio Nikolay Malkin Alexander Tong
Efficiently generating statistically independent samples from an unnormalized
probability distribution, such as equilibrium samples of many-body systems, is
a foundational problem in science. In this paper, we propose Iterated Denoising
Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic
score matching objective leveraging solely the energy function and its gradient
-- and no data samples -- to train a diffusion-based sampler. Specifically,
iDEM alternates between (I) sampling regions of high model density from a
diffusion-based sampler and (II) using these samples in our stochastic matching
objective to further improve the sampler. iDEM is scalable to high dimensions
as the inner matching objective, is simulation-free, and requires no MCMC
samples. Moreover, by leveraging the fast mode mixing behavior of diffusion,
iDEM smooths out the energy landscape enabling efficient exploration and
learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging
from standard synthetic energy functions to invariant $n$-body particle
systems. We show that the proposed approach achieves state-of-the-art
performance on all metrics and trains $2-5\times$ faster, which allows it to be
the first method to train using energy on the challenging $55$-particle
Lennard-Jones system.