Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions
This work addresses a bottleneck in generative modeling for researchers and practitioners, offering incremental improvements in flexibility and application scope.
The paper tackles the problem of fixed-step limitations in diffusion models by introducing a time-homogeneous framework that adapts steps based on noise levels, achieving improved efficiency and adaptability for tasks like conditioning and classification.
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 initialization of the denoising process and classification of noisy data.