Consistency Training with Physical Constraints

TL;DR

This paper introduces a physics-aware consistency training method that accelerates diffusion model sampling by integrating physical constraints, enabling rapid, constrained sample generation and PDE solving with deep generative models.

Contribution

It presents a novel two-stage consistency training approach that incorporates physics constraints as regularizers to improve sampling efficiency and accuracy in diffusion models.

Findings

Samples generated in a single step on toy examples

Samples adhere to physical constraints

Potential for efficient PDE solving with deep generative models

Abstract

We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2) incorporating physics constraints as a regularizer. Experiments on toy examples show that our method generates samples in a single step while adhering to the imposed constraints. This approach has the potential to efficiently solve partial differential equations (PDEs) using deep generative modeling.