Denoising diffusion models (DDMs) are state-of-the-art methods for learning densities from data across numerous domains, yet many aspects of the training and sampling pipeline remain poorly understood. In particular, noise conditioning requires practitioners to incorporate contrived unprincipled noise embeddings into neural network architectures and to use ad hoc noise schedules for sampling. To address these drawbacks, we provide a complete theory for \emph{blind denoising diffusion models} (BDDMs): a variant of DDMs where the noise amplitude is not passed into the neural network during training or sampling, obviating the need for the aforementioned design choices. We justify the correctness of BDDMs as a sampling algorithm under an assumption of low intrinsic dimensionality of the underlying data distribution relative to the ambient dimension. This assumption arises through the introduction of the Bayesian problem of estimating noise levels from a single noisy sample, which might be of independent interest. We empirically compare the performance of BDDMs to standard DDMs, showcasing the benefits of an \emph{adaptive} scheme which is rigorously justified by our analysis.

翻译：去噪扩散模型（DDMs）是当前在众多领域中从数据学习密度的最先进方法，但其训练和采样流程的许多方面仍未被充分理解。特别是，噪声调节要求从业者将人为设计的无原则噪声嵌入纳入神经网络架构，并使用针对采样的临时噪声调度。为解决这些缺陷，我们为*盲去噪扩散模型*（BDDMs）提供了完整理论：这是DDMs的一种变体，其中训练或采样过程中噪声幅度不传入神经网络，从而无需上述设计选择。我们验证了BDDMs作为采样算法的正确性，其假设底层数据分布相对于环境维度的内在低维性。这一假设源于从单个含噪样本估计噪声水平的贝叶斯问题（该问题可能具有独立研究价值）。我们通过实验将BDDMs与标准DDMs的性能进行比较，展示了由分析严格证实的*自适应*方案的优势。