提出可自适应步数的扩散模型，提升生成效率与灵活性。
Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions
- 用Doob's h-变换实现前后过程时间同质化，步数随噪声水平自适应调整。
- 在低维数据上可通过首次击中规则简化终止条件，提升采样效率。
- 预训练模型可灵活用于条件生成与噪声数据分类，适用性强。
我们提出一类新型生成扩散模型，不同于传统去噪扩散模型，该模型使加噪与去噪过程均具备时间同质性，能根据噪声水平自适应调整采样步数。通过使用Doob's h-变换对前向过程进行条件化，使过程在随机时间终止于合适的采样分布。该模型特别适用于低内在维度的数据，此时终止条件可简化为首次击中规则。其关键特性在于对目标数据的自适应能力，使得预训练的无条件生成模型可支持多种下游任务：通过适当初始化去噪过程实现自然条件生成，以及对噪声数据进行分类。
原文摘要 · Abstract (English)
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.
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