Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance

TL;DR

This paper demonstrates that breaking detailed balance in diffusion models can accelerate the generative process without altering the stationary distribution, by decomposing dynamics and constructing optimal non-reversible perturbations.

Contribution

It introduces a method to accelerate diffusion processes through non-reversible perturbations while preserving the stationary distribution, analyzing phase transitions and dynamical regimes.

Findings

Non-reversible perturbations improve relaxation rates.

Speciation time can be accelerated by suitable control.

Collapse transition remains unaffected by anti-symmetric perturbations.

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.