Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo

TL;DR

This paper introduces a novel training method for energy-based diffusion models using distillation, enabling improved control and composition in generative sampling through a Feynman Kac framework and sequential Monte Carlo methods.

Contribution

It presents a new energy training regime via distillation of diffusion models and integrates it with Feynman Kac models for enhanced sampling control and composition.

Findings

Energy functions can be effectively trained through distillation.

The Feynman Kac formalism enables composition and low-temperature sampling.

Energy-based control improves diffusion model flexibility.

Abstract

Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.