漂移核：为何扩散模型即使被要求不变也会改变输出
The Drift Kernel: Why Diffusion Models Change Even When Told Not To
该论文提出的漂移核 K_M(σ) 为量化扩散模型在空操作下的感知偏差提供了理论工具，其与解码器雅可比矩阵的关联（k_M = Tr(J_D J_D^T)）可指导视觉研究者设计更稳定的解码器或评估编辑保真度。
原文依据 We introduce the Drift Kernel K_M(sigma), defined as the expected perceptual deviation induced when running a diffusion model at noise strength sigma under a null instruction.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论即使被要求“什么都不做”，现代扩散模型也会相对于本应保留的输入微妙地改变其输出。我们将此效应称为空操作漂移。我们引入漂移核 K_M(σ)，定义为在空指令下以噪声强度 σ 运行扩散模型时引发的预期感知偏差。使用 120,000 个基线样本（SD15、SD21、SDXL 和 InstructPix2Pix 每个模型 30,000 个）和 9,600 个消融样本（四种强度，空指令与严格复制提示词对比），我们表明方差驱动的扩散模型遵循二次形式 K_M(σ) ≈ k_M σ^2 + c_M，总体 R^2 等于 0.97。我们通过解码器的泰勒展开从第一性原理推导出这种缩放关系，得到 k_M = Tr(J_D J_D^T)，它仅依赖于解码器雅可比矩阵而与提示词无关。为了验证机制结构，我们构建了合成解码器，重现了实践中看到的两种机制：二次方差驱动漂移和平坦的高方差编辑驱动漂移。我们表明提示词措辞的影响可忽略不计（系数差异小于 17%），证明漂移是结构性的而非提示词诱导的。我们发布了 NoOp-Bench，一个包含 10,000 个输入和完整代码的基准，用于可重复的核估计。额外的证明、消融、感知相似度和 CLIP 指标以及扩展可视化见补充材料。
英文原文摘要 1429 字符
Even when told to "do nothing," modern diffusion models subtly alter their output relative to the input they are supposed to preserve. We call this effect No-Op Drift. We introduce the Drift Kernel K_M(sigma), defined as the expected perceptual deviation induced when running a diffusion model at noise strength sigma under a null instruction. Using 120,000 baseline samples (30,000 per model across SD15, SD21, SDXL, and InstructPix2Pix) and 9,600 ablation samples (four strengths, null versus strict copy prompts), we show that variance-driven diffusion models follow a quadratic form K_M(sigma) approximately equal to k_M sigma^2 plus c_M, with aggregate R^2 equal to 0.97. We derive this scaling from first principles via a Taylor expansion of the decoder, yielding k_M equal to Tr(J_D J_D^T), which depends only on the decoder Jacobian and not on prompts. To validate mechanistic structure, we construct synthetic decoders that reproduce the two regimes seen in practice: quadratic variance-driven drift and flat, high-variance edit-driven drift. We show that prompt wording has negligible effect (less than 17 percent coefficient difference), proving that drift is structural and not prompt-induced. We release NoOp-Bench, a benchmark with 10,000 inputs and full code for reproducible kernel estimation. Additional proofs, ablations, LPIPS and CLIP metrics, and extended visualizations appear in the Supplementary Material.