Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance
This work addresses efficiency improvements in diffusion models for generative AI, though it appears incremental as it builds on existing phase transition analyses.
The authors tackled the problem of slow reverse processes in generative diffusion models by breaking detailed balance, which accelerates the speciation transition without altering the stationary distribution, as demonstrated with numerical experiments on Gaussian mixture models.
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.