AI 中文总结
研究针对扩散模型中无分类器指导（CFG）的分布问题，通过概率流常微分方程分析并推导解析表示，提出分布引导CFG调度，经玩具模型验证，在Stable Diffusion 1.5上改进生成效果，降低采样成本。
AI 中文摘要
无分类器指导（CFG）是扩散模型中条件生成的默认机制，但通常的乘积分布启发式方法$p_0^\omega q_0^{1-\omega}$无法捕捉其确定性引导动力学所采样的分布。我们通过概率流常微分方程分析CFG，并推导出常数和时间依赖指导下诱导分布的精确解析路径积分表示。结果公式表明CFG通过指数路径积分校正修改$p_{t_0}$，且时间依赖调度通过权重$\omega(t)-1$进入此校正。这一特性解释了分数差异如何沿采样轨迹累积，并促使提出分布引导CFG（DG-CFG）调度，该调度在考虑信号强度和低噪声分数误差放大的同时平衡时间步贡献。一个具有解析分数的玩具模型密切验证了预测分布。在Stable Diffusion 1.5上，DG-CFG改进了生成效果，并在不同指导强度下产生更强的多样性-保真度权衡，特别是在强指导导致常数和启发式调度饱和及质量下降时收益明显。在不同的NFE预算下，DG-CFG用更少的采样步骤达到固定图像质量目标，降低了实现目标指标所需的采样成本。
英文摘要
Classifier-free guidance (CFG) is the default mechanism for conditional generation in diffusion models, but the distribution sampled by its deterministic guided dynamics is not captured by the usual product-distribution heuristic $p_0^ωq_0^{1-ω}$. We analyze CFG through the probability flow ODE and derive exact analytic path-integral representations of the induced distributions for both constant and time-dependent guidance. The resulting formulas show that CFG modifies $p_{t_0}$ by an exponential path-integral correction, and that a time-dependent schedule enters this correction through the weight $ω(t)-1$. This characterization explains how score discrepancies accumulate along sampling trajectories and motivates Distribution-Guided CFG (DG-CFG), a schedule that balances timestep contributions while accounting for signal strength and low-noise score-error amplification. A toy model with analytic scores closely verifies the predicted distributions. Across Stable Diffusion~1.5, Stable Diffusion~2.1, and Stable Diffusion~XL, DG-CFG yields a stronger diversity--fidelity trade-off and robustly mitigates the saturation and quality degradation caused by strong constant or heuristic guidance. Complete NFE experiments on Stable Diffusion~1.5 and Stable Diffusion~2.1 confirm that these gains persist across sampling budgets, while fixed-quality experiments on both backbones show that DG-CFG reaches target metrics with fewer sampling steps.
