学习关键要素：通过频谱各向异性前向噪声引导扩散
Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise
AI总结：
本研究提出频谱各向异性高斯扩散（SAGD），通过调整前向噪声的频谱特性，提升扩散模型对目标分布的适应能力，并在多个视觉数据集上验证了其有效性。
摘要：
扩散概率模型（DPMs）在生成性能方面取得了显著成果，但其归纳偏置仍 largely 保持隐含。在本工作中，我们旨在将归纳偏置纳入扩散模型的训练和采样过程中，以更好地适应数据的目标分布。我们引入了一个各向异性噪声操作符，通过将各向同性的前向协方差替换为结构化的、频率对角协方差来塑造这些偏置。该操作符统一了带通掩码和幂律加权，允许我们强调或抑制指定的频率带，同时保持前向过程的高斯性。我们将此称为频谱各向异性高斯扩散（SAGD）。在本工作中，我们推导了各向异性前向协方差的分数关系，并表明，在完全支持的情况下，学习到的分数在 $t\!\to\!0$ 时收敛到真实的数据显示分数，而各向异性重塑了从噪声到数据的概率流路径。实证上，我们展示了诱导的各向异性在多个视觉数据集上优于标准扩散，并实现了选择性忽略：在学习过程中忽略已知的局限于特定带的损坏。这些结果共同表明，精心设计的各向异性前向噪声为在DPMs中定制归纳偏置提供了一个简单但原则性的处理方法。
英文摘要：
Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit. In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model. We introduce an anisotropic noise operator that shapes these biases by replacing the isotropic forward covariance with a structured, frequency-diagonal covariance. This operator unifies band-pass masks and power-law weightings, allowing us to emphasize or suppress designated frequency bands, while keeping the forward process Gaussian. We refer to this as Spectrally Anisotropic Gaussian Diffusion (SAGD). In this work, we derive the score relation for anisotropic forward covariances and show that, under full support, the learned score converges to the true data score as $t\!\to\!0$, while anisotropy reshapes the probability-flow path from noise to data. Empirically, we show the induced anisotropy outperforms standard diffusion across several vision datasets, and enables selective omission: learning while ignoring known corruptions confined to specific bands. Together, these results demonstrate that carefully designed anisotropic forward noise provides a simple, yet principled, handle to tailor inductive bias in DPMs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
