PID-controlled Langevin Dynamics for Faster Sampling of Generative Models

2025-11-16

AI Summary

Langevin dynamics sampling suffers from extremely low generation speed due to the requirement of numerous fine-grained iterative steps. To address this, we propose PID-controlled Langevin Dynamics (PIDLD), the first method to incorporate proportional-integral-derivative (PID) control into generative model sampling. PIDLD dynamically adjusts the step size using instantaneous energy gradient feedback (P), historical accumulation (I), and trend estimation of gradient changes (D), enabling adaptive and stable sampling trajectories without additional training or data. Our approach significantly reduces the number of sampling steps—by 40–60% on average—while simultaneously improving sample quality and convergence robustness. We validate PIDLD on image generation and inverse inference tasks, demonstrating consistent performance gains across diverse settings. This work establishes a novel paradigm for accelerating score-based generative models through principled control-theoretic design.

Technology Category

• Natural Language Processing: Generation
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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}.

Problem

• Accelerates slow Langevin dynamics sampling for generative models
• Reduces iteration count while maintaining high sample quality
• Requires no retraining and integrates with existing Langevin methods

Innovation

• PID control uses historical gradients and trends
• Algorithm reduces iterations without extra training
• Method accelerates sampling in Langevin-based models