修复分类器自由指导在高引导强度下的不稳定问题，无需额外计算成本。
Guidance Breaks the Fitted Operator: A Terminal-Fitted Repair for Classifier-Free Guidance
- 提出基于终端拟合的修正方法，替换原引导项以稳定采样过程。
- 在低噪声区域消除残差发散，实现与精确引导流的一阶精度匹配。
- 适用于高引导强度场景，尤其适合图像生成中需稳定性的任务。
分类器自由指导（CFG）是扩散模型和流匹配采样器中强化类别条件的标准方法，但在高引导强度下会过度饱和并导致不稳定性，从业者通常通过增加采样步数或限制间隔调度来缓解。本文从渐近保持、数值分析角度分析CFG，基于近期结果：确定性DDIM步骤是无引导终端层的唯一拟合算子，在最终小噪声区间精确成立。我们发现，引导会使判别子空间重新刚化为异常指数1+w，使DDIM在此处不再拟合，且在粗网格上，其引导残差随sigma_min趋于零而发散。我们证明了一个具有三个有序步长阈值的引导时钟屏障，并将单步过饱和视为其终点——这是校准模型上的求解器伪影，而非连续引导律本身。该分析导出一种仅需一系数、无需额外计算量的修复方案：将CFG中的w(r-1)替换为r^(1+w)-r作为引导方向。在判别交叉点上，此方法可消除CFG的sigma_min发散爆炸，并在sigma_min→0时对精确引导流保持一阶精度。在学习过的CIFAR-10检查点及作为跨域烟雾测试的Stable Diffusion 1.5 DDIM上，它在无额外成本下成为高引导强度下的稳定器，而非通用质量调节器：减少残差放大和饱和，9/9点上获得优于CFG的FID表现，同时在困难单元块中保持分类器代理目标准确率。我们也报告了其局限性：并非普遍提升图像质量，且相较于密集的基线CFG，也不是该场域的统一更优积分器。
原文摘要 · Abstract (English)
Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules. We analyze CFG through an asymptotic-preserving, numerical-analysis lens. Building on a recent result that the deterministic DDIM step is the unique fitted operator for the unguided terminal layer, exact on the final small-sigma stretch of sampling, we show that guidance re-stiffens exactly the discriminative subspace to an anomalous exponent 1+w. DDIM is therefore no longer fitted there, and on coarse meshes its guided residual diverges as sigma_min goes to zero. We prove a guided clock barrier with three ordered step-size thresholds, and read one-step oversaturation as its endpoint: a solver artifact on the calibration model rather than the continuous guided law. The same analysis yields a one-coefficient, zero-extra-NFE repair: replace CFG's w(r-1) by r^(1+w)-r on the guidance direction. On the calibration model's discriminative crossover, this removes CFG's sigma_min-divergent blow-up and is first-order accurate against the exact guided flow as sigma_min goes to zero. On learned CIFAR-10 checkpoints, and as a cross-domain smoke test on Stable Diffusion 1.5 DDIM, it acts as a high-guidance stabilizer at no extra cost rather than a universal quality knob: it cuts residual amplification and saturation, gives 9/9 point-FID wins over CFG on the tested grid, and preserves classifier-proxy target accuracy in the hard-cell blocks. We report the limits alongside: it is not a universal image-quality win, and against a dense vanilla-CFG reference it is not a uniformly better integrator of that field.
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