PID-controlled Langevin Dynamics for Faster Sampling of Generative Models

TL;DR

This paper introduces PID-controlled Langevin Dynamics (PIDLD), a control-theoretic method that accelerates sampling in generative models by reducing iterations without additional training, improving efficiency and quality.

Contribution

We propose PIDLD, a novel control-based acceleration method for Langevin dynamics that requires no extra training and enhances sampling efficiency across tasks.

Findings

PIDLD reduces the number of iterations needed for high-quality sampling.

The method improves sampling speed without sacrificing quality.

Extensive experiments validate the effectiveness of PIDLD across tasks.

Abstract

Langevin dynamics sampling suffers from extremely low generation speed, fundamentally limited by numerous fine-grained iterations to converge to the target distribution. We introduce PID-controlled Langevin Dynamics (PIDLD), a novel sampling acceleration algorithm that reinterprets the sampling process using control-theoretic principles. By treating energy gradients as feedback signals, PIDLD combines historical gradients (the integral term) and gradient trends (the derivative term) to efficiently traverse energy landscapes and adaptively stabilize, thereby significantly reducing the number of iterations required to produce high-quality samples. Our approach requires no additional training, datasets, or prior information, making it immediately integrable with any Langevin-based method. Extensive experiments across image generation and reasoning tasks demonstrate that PIDLD achieves higher quality with fewer steps, making Langevin-based generative models more practical for efficiency-critical applications. The implementation can be found at \href{https://github.com/tsinghua-fib-lab/PIDLD}{https://github.com/tsinghua-fib-lab/PIDLD}.