提出新引导调度方法，提升扩散模型生成质量与多样性。
Analytic Distribution of Classifier-Free Guidance for Schedule Design
- 基于概率流微分方程推导出引导分布的精确解析表达式。
- 新调度方法在多模型上实现更优的保真度-多样性权衡，减少质量退化。
- 适合需要高质量图像生成且关注采样效率的研究者与应用者。
Classifier-free guidance（CFG）是扩散模型中条件生成的默认机制，但其确定性引导动态所采样的分布无法用常规的乘积分布启发式 $p_0^ωq_0^{1-ω}$ 描述。本文通过概率流常微分方程分析 CFG，推导出恒定与时变引导权重下诱导分布的精确路径积分表示。结果表明，CFG 通过对初始分布 $p_{t_0}$ 施加指数路径积分修正来改变分布，而时变调度通过权重 $ω(t)-1$ 影响该修正。这一表征解释了得分差异沿采样轨迹的累积机制，并催生了分布引导的 CFG（DG-CFG），其能平衡各时间步贡献，同时考虑信号强度与低噪声得分误差放大。一个具有解析得分的简化模型验证了预测分布的准确性。在 Stable Diffusion 1.5、2.1 和 XL 上，DG-CFG 在多样性和保真度之间取得更强权衡，有效缓解强恒定或启发式引导导致的饱和与质量下降。对 Stable Diffusion 1.5 与 2.1 的完整 NFE 实验表明，这些优势在不同采样预算下均成立；固定质量实验显示，DG-CFG 能以更少采样步骤达到目标指标。
原文摘要 · Abstract (English)
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.
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