通过破坏细致平衡，加速扩散模型的生成速度而不改变最终分布。
Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance
- 引入非可逆项产生旋转概率流，打破细致平衡以加速反向过程。
- 理论证明非可逆扰动能加快物种分化时间，但对坍缩时间无影响。
- 适用于希望提升生成效率又不改变分布特性的扩散模型研究者。
我们表明，在生成式扩散过程中故意破坏细致平衡，可在不改变稳态分布的前提下加速反向过程。以奥恩斯坦-乌伦贝克过程为例，将动力学分解为对称分量与非可逆反称分量，后者生成旋转概率流。我们构造出指数最优的非可逆扰动，提升了长期松弛速率，同时保持目标稳态分布不变。分析显示，此类非可逆控制能重塑最近在生成式扩散模型中识别出的相变宏观动力学行为。推导出物种分化时间的一般判据，表明合适的非可逆扰动可加速分化。相反，坍缩相变由对称分量决定的迹控制相空间收缩机制主导，对应坍缩时间在反称扰动下保持不变。高斯混合模型上的数值实验验证了上述结论。
原文摘要 · Abstract (English)
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.
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