Energy-based diffusion generator for efficient sampling of Boltzmann distributions.

Area of Science:

• Computational Physics
• Machine Learning
• Statistical Mechanics

Background:

• Sampling from Boltzmann distributions is crucial but challenging for complex energy functions.
• Existing methods often require simulations or impose restrictive network constraints.

Purpose of the Study:

• To present a novel, simulation-free approach for sampling complex Boltzmann distributions.
• To develop a flexible and high-performing generative model for statistical sampling.

Main Methods:

• The Energy-Based Diffusion Generator (EDG) integrates variational autoencoders and diffusion models.
• A decoder generates samples from latent variables, while a diffusion encoder estimates KL divergence.
• The method is simulation-free, avoiding differential equation solving during training.

Main Results:

• EDG demonstrates superior performance across various sampling tasks with complex target distributions.
• Empirical evaluations show outperformance compared to existing sampling methods.
• Flexible network design is enabled by removing constraints like decoder bijectivity.

Conclusions:

• EDG offers an effective and flexible simulation-free solution for sampling complex Boltzmann distributions.
• The approach advances generative modeling for statistical and scientific applications.
• EDG represents a significant improvement over current state-of-the-art sampling techniques.