We analyze, theoretically and empirically, the performance of generative diffusion models based on \emph{blind denoisers}, in which the denoiser is not given the noise amplitude in either the training or sampling processes. Assuming that the data distribution has low intrinsic dimensionality, we prove that blind denoising diffusion models (BDDMs), despite not having access to the noise amplitude, \emph{automatically} track a particular \emph{implicit} noise schedule along the reverse process. Our analysis shows that BDDMs can accurately sample from the data distribution in polynomially many steps as a function of the intrinsic dimension. Empirical results corroborate these mathematical findings on both synthetic and image data, demonstrating that the noise variance is accurately estimated from the noisy image. Remarkably, we observe that schedule-free BDDMs produce samples of higher quality compared to their non-blind counterparts. We provide evidence that this performance gain arises because BDDMs correct the mismatch between the true residual noise (of the image) and the noise assumed by the schedule used in non-blind diffusion models.

翻译：我们从理论和实证两方面分析了基于**盲去噪器**的生成扩散模型的性能，其中去噪器在训练和采样过程中均未获得噪声幅值信息。假设数据分布具有低本征维度，我们证明盲去噪扩散模型尽管无法访问噪声幅值，却能在逆向过程中**自动**追踪一个特定的**隐式**噪声调度。我们的分析表明，盲去噪扩散模型能够以本征维度的多项式函数步数精确地从数据分布中采样。在合成数据和图像数据上的实证结果均验证了这些数学结论，表明噪声方差可从含噪图像中准确估计。值得注意的是，我们观察到无调度约束的盲去噪扩散模型相比非盲模型能生成更高质量的样本。我们提供的证据表明，这种性能提升源于盲去噪扩散模型修正了真实残差噪声（图像的）与非盲扩散模型所用调度假设噪声之间的失配。