Diffusion-based image generative models produce high-fidelity images through iterative denoising but remain vulnerable to memorization, where they unintentionally reproduce exact copies or parts of training images. Recent memorization detection methods are primarily based on the norm of score difference as indicators of memorization. We prove that such norm-based metrics are mainly effective under the assumption of isotropic log-probability distributions, which generally holds at high or medium noise levels. In contrast, analyzing the anisotropic regime reveals that memorized samples exhibit strong angular alignment between the guidance vector and unconditional scores in the low-noise setting. Through these insights, we develop a memorization detection metric by integrating isotropic norm and anisotropic alignment. Our detection metric can be computed directly on pure noise inputs via two conditional and unconditional forward passes, eliminating the need for costly denoising steps. Detection experiments on Stable Diffusion v1.4 and v2 show that our metric outperforms existing denoising-free detection methods while being at least approximately 5x faster than the previous best approach. Finally, we demonstrate the effectiveness of our approach by utilizing a mitigation strategy that adapts memorized prompts based on our developed metric. The code is available at https://github.com/rohanasthana/memorization-anisotropy .

翻译：基于扩散的图像生成模型通过迭代去噪生成高保真图像，但仍存在记忆化问题，即无意中复现训练图像的完整副本或局部片段。现有的记忆化检测方法主要基于分数差异的范数作为记忆化指标。我们证明，此类基于范数的度量主要在对数概率分布各向同性的假设下有效，该假设通常在高或中等噪声水平下成立。相比之下，对各向异性区域的分析表明，在低噪声设置中，记忆化样本的引导向量与无条件分数之间存在强烈的角度对齐特征。基于这些发现，我们通过整合各向同性范数与各向异性对齐度，构建了一种记忆化检测度量。该检测度量可直接在纯噪声输入上通过两次条件与无条件前向传播计算，无需昂贵的去噪步骤。在Stable Diffusion v1.4和v2上的检测实验表明，我们的度量优于现有的免去噪检测方法，同时比先前最佳方法提速约5倍以上。最后，我们通过基于所开发度量调整记忆化提示词的缓解策略，验证了该方法的有效性。代码发布于https://github.com/rohanasthana/memorization-anisotropy。