Consistency Training with Physical Constraints

TL;DR

The paper tackles the challenge of slow sampling in diffusion models when physical constraints must be satisfied. It introduces CT-Physics, a two-stage framework that combines Consistency Training with physics-based regularization to enable fast, constraint-compliant generation. The approach replaces the traditional denoiser with a one-step CT denoiser and adds a residual term enforcing PDE constraints, validated on toy examples that show one- to two-step sampling while respecting physics. This work suggests a practical direction for using deep generative models to efficiently solve PDEs and generate physics-consistent data.

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.

Figures (2)

• Figure 1: Results of CT-Physics on the toy examples. Red dots: model samples, black dashed line: $\bm{\mathcal{R}}({\mathbf{x}}_0) = 0$.
• Figure 2: Sampling results of only using Stage 2 training. Red dots: model samples, black dashed line: unit circle. The model fails to capture the original data distribution.