🤖 AI Summary
Sampling from Boltzmann distributions governed by high-dimensional, complex energy functions remains challenging due to the computational cost of traditional dynamics-based methods. To address this, we propose EDG—a generative framework that bypasses explicit dynamical simulation entirely. EDG integrates variational autoencoding with diffusion modeling: it employs a non-bijective decoder to enhance modeling expressivity and introduces a diffusion-based encoder to accurately estimate the KL divergence in latent space, enabling stable and efficient distribution matching. Crucially, EDG establishes the first “simulation-free” training paradigm, eliminating the need for solving differential equations or running Markov chain Monte Carlo. Evaluated on diverse complex Boltzmann sampling tasks—including molecular conformational sampling and spin-glass inference—EDG consistently outperforms state-of-the-art energy-based and generative models, achieving superior sampling efficiency and training stability. This work introduces a novel, scalable paradigm for modeling high-dimensional physical systems governed by Boltzmann statistics.
📝 Abstract
Sampling from Boltzmann distributions, particularly those tied to high-dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel approach that integrates ideas from variational autoencoders and diffusion models. EDG leverages a decoder to transform latent variables from a simple distribution into samples approximating the target Boltzmann distribution, while the diffusion-based encoder provides an accurate estimate of the Kullback-Leibler divergence during training. Notably, EDG is simulation-free, eliminating the need to solve ordinary or stochastic differential equations during training. Furthermore, by removing constraints such as bijectivity in the decoder, EDG allows for flexible network design. Through empirical evaluation, we demonstrate the superior performance of EDG across a variety of complex distribution tasks, outperforming existing methods.