We introduce a new class of generative diffusion models that, unlike conventional denoising diffusion models, achieve a time-homogeneous structure for both the noising and denoising processes, allowing the number of steps to adaptively adjust based on the noise level. This is accomplished by conditioning the forward process using Doob's $h$-transform, which terminates the process at a suitable sampling distribution at a random time. The model is particularly well suited for generating data with lower intrinsic dimensions, as the termination criterion simplifies to a first-hitting rule. A key feature of the model is its adaptability to the target data, enabling a variety of downstream tasks using a pre-trained unconditional generative model. These tasks include natural conditioning through appropriate initialisation of the denoising process and classification of noisy data.

翻译：我们提出了一类新的生成扩散模型，与传统的去噪扩散模型不同，该模型在加噪和去噪过程中均实现了时间齐次结构，从而允许步数根据噪声水平自适应调整。这是通过利用Doob的$h$-变换对前向过程进行条件化实现的，该变换会在随机时间以合适的采样分布终止过程。该模型特别适用于生成具有较低本征维度的数据，因为终止准则可简化为首次到达规则。该模型的一个关键特性是其对目标数据的自适应性，使得预训练的无条件生成模型能够支持多种下游任务。这些任务包括通过适当初始化去噪过程实现自然条件生成，以及对含噪数据进行分类。