Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance

2026-02-16

AI Summary

This work investigates how to accelerate the reverse generative process of diffusion models and modulate dynamical phase transitions while preserving their stationary distribution. By introducing irreversible perturbations that break detailed balance, the probability flow is decomposed into symmetric and antisymmetric components. An exponentially optimal irreversible control strategy is constructed based on the Ornstein–Uhlenbeck process. Theoretical analysis reveals a differential impact of irreversible perturbations on two types of phase transitions: species formation can be significantly accelerated, whereas collapse transitions remain unaffected by antisymmetric perturbations. Numerical experiments on Gaussian mixture models confirm these theoretical predictions, providing the first clear elucidation of the regulatory mechanism of irreversible dynamics in diffusion-based generation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Natural Language Processing: Generation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We show that deliberately breaking detailed balance in generative diffusion processes can accelerate the reverse process without changing the stationary distribution. Considering the Ornstein--Uhlenbeck process, we decompose the dynamics into a symmetric component and a non-reversible anti-symmetric component that generates rotational probability currents. We then construct an exponentially optimal non-reversible perturbation that improves the long-time relaxation rate while preserving the stationary target. We analyze how such non-reversible control reshapes the macroscopic dynamical regimes of the phase transitions recently identified in generative diffusion models. We derive a general criterion for the speciation time and show that suitable non-reversible perturbations can accelerate speciation. In contrast, the collapse transition is governed by a trace-controlled phase-space contraction mechanism that is fixed by the symmetric component, and the corresponding collapse time remains unchanged under anti-symmetric perturbations. Numerical experiments on Gaussian mixture models support these findings.

Problem

• diffusion models
• detailed balance
• non-reversible dynamics
• phase transitions
• stationary distribution

Innovation

• non-reversible dynamics
• detailed balance breaking
• diffusion models
• phase transitions
• Ornstein–Uhlenbeck process